Wyniki wyszukiwania dla: domination
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Paired domination and doubly domination in graphs
PublikacjaW rozprawie poruszane są zagadnienia związane z dominowaniem parami w grafach oraz domiowaniem totalno - powściągniętym w grafach. Ponadto omawiane są zagadnienia związane ze złożonością obliczeniową różnych problemów dominowania w grafach.
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Domination subdivision and domination multisubdivision numbers of graphs
PublikacjaThe domination subdivision number sd(G) of a graph G is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the domination number of G. It has been shown [10] that sd(T)<=3 for any tree T. We prove that the decision problem of the domination subdivision number is NP-complete even for bipartite graphs. For this reason we define the domination multisubdivision number...
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Graphs with equal domination and certified domination numbers
PublikacjaA setDof vertices of a graphG= (VG,EG) is a dominating set ofGif every vertexinVG−Dis adjacent to at least one vertex inD. The domination number (upper dominationnumber, respectively) ofG, denoted byγ(G) (Γ(G), respectively), is the cardinality ofa smallest (largest minimal, respectively) dominating set ofG. A subsetD⊆VGis calleda certified dominating set ofGifDis a dominating set ofGand every vertex inDhas eitherzero...
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Total Domination Versus Domination in Cubic Graphs
PublikacjaA dominating set in a graph G is a set S of vertices of G such that every vertex not in S has a neighbor in S. Further, if every vertex of G has a neighbor in S, then S is a total dominating set of G. The domination number,γ(G), and total domination number, γ_t(G), are the minimum cardinalities of a dominating set and total dominating set, respectively, in G. The upper domination number, \Gamma(G), and the upper total domination...
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Total domination in versus paired-domination in regular graphs
PublikacjaA subset S of vertices of a graph G is a dominating set of G if every vertex not in S has a neighbor in S, while S is a total dominating set of G if every vertex has a neighbor in S. If S is a dominating set with the additional property that the subgraph induced by S contains a perfect matching, then S is a paired-dominating set. The domination number, denoted γ(G), is the minimum cardinality of a dominating set of G, while the...
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The paired-domination and the upper paired-domination numbers of graphs
PublikacjaIn this paper we obtain the upper bound for the upper paired-domination number and we determine the extremal graphs achieving this bound. Moreover we determine the upper paired- domination number for cycles.
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Graphs with equal domination and 2-distance domination numbers
PublikacjaW publikacji scharakteryzowane są wszystkie te drzewa i grafy jednocykliczne, w których liczba dominowania oraz liczba 2-dominowania na odległość są sobie równe.
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Paired domination versus domination and packing number in graphs
PublikacjaGiven a graph G = (V(G), E(G)), the size of a minimum dominating set, minimum paired dominating set, and a minimum total dominating set of a graph G are denoted by γ (G), γpr(G), and γt(G), respectively. For a positive integer k, a k-packing in G is a set S ⊆ V(G) such that for every pair of distinct vertices u and v in S, the distance between u and v is at least k + 1. The k-packing number is the order of a largest kpacking and...
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Certified domination
PublikacjaImagine that we are given a set D of officials and a set W of civils. For each civil x ∈ W, there must be an official v ∈ D that can serve x, and whenever any such v is serving x, there must also be another civil w ∈ W that observes v, that is, w may act as a kind of witness, to avoid any abuse from v. What is the minimum number of officials to guarantee such a service, assuming a given social network? In this paper, we introduce...
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On trees with equal domination and total outer-independent domination numbers
PublikacjaFor a graph G=(V,E), a subset D subseteq V(G) is a dominating set if every vertex of V(G)D has a neighbor in D, while it is a total outer-independent dominating set if every vertex of G has a neighbor in D, and the set V(G)D is independent. The domination (total outer-independent domination, respectively) number of G is the minimum cardinality of a dominating (total outer-independent dominating, respectively) set of G. We characterize...
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Trees with equal restrained domination and total restrained domination numbers
PublikacjaW publikacji scharakteryzowano wszystkie drzewa, w których liczby dominowania powściągniętego oraz podwójnie totalnego są sobie równe.
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On trees with equal 2-domination and 2-outer-independent domination numbers
PublikacjaFor a graph G = (V,E), a subset D \subseteq V(G) is a 2-dominating set if every vertex of V(G)\D$ has at least two neighbors in D, while it is a 2-outer-independent dominating set if additionally the set V(G)\D is independent. The 2-domination (2-outer-independent domination, respectively) number of G, is the minimum cardinality of a 2-dominating (2-outer-independent dominating, respectively) set of G. We characterize all trees...
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On trees with double domination number equal to 2-domination number plus one
PublikacjaA vertex of a graph is said to dominate itself and all of its neighbors. A subset D subseteq V(G) is a 2-dominating set of G if every vertex of V(G)D is dominated by at least two vertices of D, while it is a double dominating set of G if every vertex of G is dominated by at least two vertices of D. The 2-domination (double domination, respectively) number of a graph G is the minimum cardinality of a 2-dominating (double dominating,...
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On the ratio between 2-domination and total outer-independent domination numbers of trees
PublikacjaA 2-dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)D has a at least two neighbors in D. A total outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V(G)D is independent. The 2-domination (total outer-independent domination, respectively) number of a graph G is the minimum cardinality of a 2-dominating (total...
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On trees with double domination number equal to total domination number plus one
PublikacjaA total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. A vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The total (double, respectively) domination number of a graph G is the minimum cardinality of a total (double,...
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Independent Domination Subdivision in Graphs
PublikacjaA set $S$ of vertices in a graph $G$ is a dominating set if every vertex not in $S$ is adjacent to a vertex in~$S$. If, in addition, $S$ is an independent set, then $S$ is an independent dominating set. The independent domination number $i(G)$ of $G$ is the minimum cardinality of an independent dominating set in $G$. The independent domination subdivision number $\sdi(G)$ is the minimum number of edges that must be subdivided (each...
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Secure Italian domination in graphs
PublikacjaAn Italian dominating function (IDF) on a graph G is a function f:V(G)→{0,1,2} such that for every vertex v with f(v)=0, the total weight of f assigned to the neighbours of v is at least two, i.e., ∑u∈NG(v)f(u)≥2. For any function f:V(G)→{0,1,2} and any pair of adjacent vertices with f(v)=0 and u with f(u)>0, the function fu→v is defined by fu→v(v)=1, fu→v(u)=f(u)−1 and fu→v(x)=f(x) whenever x∈V(G)∖{u,v}. A secure Italian dominating...
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The limit case of a domination property
PublikacjaPraca dotyczy dolnego ograniczenia liczby dominowania w grafach, ze względu na ilość wierzchołków oraz największą liczbę liści w drzewie spinającym.
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On trees with double domination number equal to 2-outer-independent domination number plus one
PublikacjaA vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G is the minimum cardinality of a double dominating set of G. For a graph G=(V,E), a subset D subseteq V(G) is a 2-dominating set if every vertex of V(G)D has at least two neighbors...
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2-outer-independent domination in graphs
PublikacjaWe initiate the study of 2-outer-independent domination in graphs. A 2-outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)\D has at least two neighbors in D, and the set V(G)\D is independent. The 2-outer-independent domination number of a graph G is the minimum cardinality of a 2-outer-independent dominating set of G. We show that if a graph has minimum degree at least two,...
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Coronas and Domination Subdivision Number of a Graph
PublikacjaIn this paper, for a graph G and a family of partitions P of vertex neighborhoods of G, we define the general corona G ◦P of G. Among several properties of this new operation, we focus on application general coronas to a new kind of characterization of trees with the domination subdivision number equal to 3.
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Interpolation properties of domination parameters of a graph
PublikacjaAn integer-valued graph function π is an interpolating function if a set π(T(G))={π(T): T∈TT(G)} consists of consecutive integers, where TT(G) is the set of all spanning trees of a connected graph G. We consider the interpolation properties of domination related parameters.
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On the connected and weakly convex domination numbers
PublikacjaIn this paper we study relations between connected and weakly convex domination numbers. We show that in general the difference between these numbers can be arbitrarily large and we focus on the graphs for which a weakly convex domination number equals a connected domination number. We also study the influence of the edge removing on the weakly convex domination number, in particular we show that a weakly convex domination number...
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On domination multisubdivision number of unicyclic graphs
PublikacjaThe paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram, S.M. Sheikholeslami, O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009), 622–628], we constructively characterize all connected unicyclic graphs with...
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TOTAL DOMINATION MULTISUBDIVISION NUMBER OF A GRAPH
PublikacjaThe domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G. Similarly we define the total domination multisubdivision number msd_t (G) of a graph G and we show that for any connected graph G of order at least two, msd_t (G) ≤ 3. We show that for trees the total domination...
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Complexity Issues on of Secondary Domination Number
PublikacjaIn this paper we study the computational complexity issues of the problem of secondary domination (known also as (1, 2)-domination) in several graph classes. We also study the computational complexity of the problem of determining whether the domination and secondary domination numbers are equal. In particular, we study the influence of triangles and vertices of degree 1 on these numbers. Also, an optimal algorithm for finding...
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The convex domination subdivision number of a graph
PublikacjaLet G = (V;E) be a simple graph. A set D\subset V is a dominating set of G if every vertex in V - D has at least one neighbor in D. The distance d_G(u, v) between two vertices u and v is the length of a shortest (u, v)-path in G. An (u, v)-path of length d_G(u; v) is called an (u, v)-geodesic. A set X\subset V is convex in G if vertices from all (a, b)-geodesics belong to X for any two vertices a, b \in X. A set X is a convex dominating...
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Weakly connected Roman domination in graphs
PublikacjaA Roman dominating function on a graph G=(V,E) is defined to be a function f :V → {0,1,2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v)=2. A dominating set D⊆V is a weakly connected dominating set of G if the graph (V,E∩(D×V)) is connected. We define a weakly connected Roman dominating function on a graph G to be a Roman dominating function such that the set...
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On the total restrained domination number of a graph
PublikacjaW pracy przedstawione są ograniczenia i własności liczby dominowania podwójnie totalnego.
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Distance paired domination numbers of graphs
PublikacjaW pracy przedstawione są pewne własności liczb k-dominowania parami w grafach. Wykazane jest, że problem decyzyjny liczby k-dominowania parami jest problemem NP-zupełnym nawet dla grafów dwudzielnych. Przedstawione są ograniczenia górne i dolne dla liczby k-dominowania parami w drzewach i scharakteryzowane drzewa, w których te ograniczenia są osiągnięte.
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Weakly connected domination subdivision numbers
PublikacjaLiczba podziału krawędzi dla dominowania słabo spójnego to najmniejsza liczba krawędzi jaką należy podzielić, aby wzrosła liczba dominowania słabo wypukłego. W pracy przedstawione są własności liczby podziału krawędzi dla dominowania słabo spójnego dla różnych grafów.
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Weakly connected domination critical graphs
PublikacjaPraca dotyczy niektórych klas grafów krytycznych ze względu na liczbę dominowania słabo spójnego.
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Total outer-connected domination in trees
PublikacjaW pracy przedstawiono dolne ograniczenie na liczbę dominowania totalnego zewnętrznie spójnego w grafach oraz scharakteryzowano wszystkie drzewa osiągające to ograniczenie.
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The outer-connected domination number of a graph
PublikacjaW pracy została zdefiniowana liczba dominowania zewnętrznie spójnego i przedstawiono jej podstawowe własności.
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Total restrained domination numbers of trees
PublikacjaOpisane są wszystkie drzewa, w których liczby dominowania totalnego i totalno - powściągniętego są sobie równe, a także podano dolne ograniczenie na liczbę dominowania totalno - powściągniętego w drzewach.
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Lower bound on the domination number of a tree.
PublikacjaW pracy przedstawiono dolne ograniczenie na liczbę dominowania w drzewach oraz przedstawiono pełną charakterystykę grafów ekstremalnych.
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Weakly convex and convex domination numbers.
PublikacjaW artykule przedstawione są nowo zdefiniowane liczby dominowania wypukłego i słabo wypukłego oraz ich porównanie z innymi liczbami dominowania. W szczególności, rozważana jest równość liczby dominowania spójnego i wypukłego dla grafów kubicznych.
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On the doubly connected domination number of a graph
PublikacjaW pracy została zdefiniowana liczba dominowania podwójnie spójnego i przedstawiono jej podstawowe własności.
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Domination-Related Parameters in Rooted Product Graphs
PublikacjaAbstract A set S of vertices of a graph G is a dominating set in G if every vertex outside of S is adjacent to at least one vertex belonging to S. A domination parameter of G is related to those sets of vertices of a graph satisfying some domination property together with other conditions on the vertices of G. Here, we investigate several domination-related parameters in rooted product graphs.
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Paired domination subdivision and multisubdivision numbers of graphs
PublikacjaThe paired domination subdivision number sdpr(G) of a graph G is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the paired domination number of G. We prove that the decision problem of the paired domination subdivision number is NP-complete even for bipartite graphs. For this reason we define the paired domination muttisubdivision number of a nonempty graph...
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Influence of edge subdivision on the convex domination number
PublikacjaWe study the influence of edge subdivision on the convex domination number. We show that in general an edge subdivision can arbitrarily increase and arbitrarily decrease the convex domination number. We also find some bounds for unicyclic graphs and we investigate graphs G for which the convex domination number changes after subdivision of any edge in G.
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Weakly convex domination subdivision number of a graph
PublikacjaA set X is weakly convex in G if for any two vertices a; b \in X there exists an ab–geodesic such that all of its vertices belong to X. A set X \subset V is a weakly convex dominating set if X is weakly convex and dominating. The weakly convex domination number \gamma_wcon(G) of a graph G equals the minimum cardinality of a weakly convex dominating set in G. The weakly convex domination subdivision number sd_wcon (G) is the minimum...
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On the super domination number of lexicographic product graphs
PublikacjaThe neighbourhood of a vertexvof a graphGis the setN(v) of all verticesadjacent tovinG. ForD⊆V(G) we defineD=V(G)\D. A setD⊆V(G) is called a super dominating set if for every vertexu∈D, there existsv∈Dsuch thatN(v)∩D={u}. The super domination number ofGis theminimum cardinality among all super dominating sets inG. In this article weobtain closed formulas and tight bounds for the super dominating number oflexicographic product...
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Bounds on the vertex-edge domination number of a tree
PublikacjaA vertex-edge dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every edge of $G$ is incident with a vertex of $D$ or a vertex adjacent to a vertex of $D$. The vertex-edge domination number of a graph $G$, denoted by $\gamma_{ve}(T)$, is the minimum cardinality of a vertex-edge dominating set of $G$. We prove that for every tree $T$ of order $n \ge 3$ with $l$ leaves and $s$ support vertices we have $(n-l-s+3)/4...
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Bipartite theory of graphs: outer-independent domination
PublikacjaLet $G = (V,E)$ be a bipartite graph with partite sets $X$ and $Y$. Two vertices of $X$ are $X$-adjacent if they have a common neighbor in $Y$, and they are $X$-independent otherwise. A subset $D \subseteq X$ is an $X$-outer-independent dominating set of $G$ if every vertex of $X \setminus D$ has an $X$-neighbor in $D$, and all vertices of $X \setminus D$ are pairwise $X$-independent. The $X$-outer-independent domination number...
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Isolation Number versus Domination Number of Trees
PublikacjaIf G=(VG,EG) is a graph of order n, we call S⊆VG an isolating set if the graph induced by VG−NG[S] contains no edges. The minimum cardinality of an isolating set of G is called the isolation number of G, and it is denoted by ι(G). It is known that ι(G)≤n3 and the bound is sharp. A subset S⊆VG is called dominating in G if NG[S]=VG. The minimum cardinality of a dominating set of G is the domination number, and it is denoted by γ(G)....
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Total outer-connected domination numbers of trees
PublikacjaNiech G=(V,E) będzie grafem bez wierzchołków izolowanych. Zbiór wierzchołków D nazywamy zbiorem dominującym totalnym zewnętrznie spójnym jeżli każdy wierzchołek grafu ma sąsiada w D oraz podgraf indukowany przez V-D jest grafem spójnym. Moc najmniejszego zbioru D o takich własnościach nazywamy liczbą dominowania totalnego zewnątrznie spójnego. Praca m.in. zawiera dolne ograniczenie na liczbę dominowania totalnego zewnętrznie spójnego...
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Lower bound on the paired domination number of a tree
PublikacjaW pracy przedstawione jest ograniczenie dolne dla liczby dominowania parami oraz scharakteryzowane są wszystkie drzewa ekstremalne.
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Weakly connected domination stable trees [online]
PublikacjaPraca dotyczy pełnej charakteryzacji drzew stabilnych ze względu na liczbę dominowania słabo spójnego.
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Strong weakly connected domination subdivisible graphs
PublikacjaArtykuł dotyczy wpływu podziału krawędzi na liczbę dominowania słabo spójnego. Charakteryzujemy grafy dla których podział dowolnej krawędzi zmienia liczbę dominowania słabo spójnego oraz grafy dla których podział dowolnych dwóch krawędzi powoduje zmianę liczby dominowania słabo spójnego.
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Graphs with convex domination number close to their order
PublikacjaW pracy opisane są grafy z liczbą dominowania wypukłego bliską ilości ich wierzchołków.
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On trees attaining an upper bound on the total domination number
PublikacjaA total dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D. The total domination number of a graph G, denoted by γ_t(G), is the minimum cardinality of a total dominating set of G. Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International Journal of Graphs and Combinatorics 1 (2004), 69-75] established the following upper bound on the total domination...
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Relations between the domination parameters and the chromatic index of a graph
PublikacjaIn this paper we show bounds for the sum and the product of the domination parameters and the chromatic index of a graph. We alsopresent some families of graphs for which these bounds are achieved.
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Block graphs with large paired domination multisubdivision number
PublikacjaThe paired domination multisubdivision number of a nonempty graph G, denoted by msdpr(G), is the smallest positive integer k such that there exists an edge which must be subdivided k times to increase the paired domination number of G. It is known that msdpr(G) ≤ 4 for all graphs G. We characterize block graphs with msdpr(G) = 4.
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Cops, a fast robber and defensive domination on interval graphs
PublikacjaThe game of Cops and ∞-fast Robber is played by two players, one controlling c cops, the other one robber. The players alternate in turns: all the cops move at once to distance at most one each, the robber moves along any cop-free path. Cops win by sharing a vertex with the robber, the robber by avoiding capture indefinitely. The game was proposed with bounded robber speed by Fomin et al. in “Pursuing a fast robber on a graph”,...
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Domination numbers in graphs with removed edge or set of edges
PublikacjaW artykule przedstawiony jest wpływ usuwania krawędzi lub zbioru krawędzi na liczby dominowania spójnego i słabo spójnego.
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Nordhaus-Gaddum results for the convex domination number of a graph
PublikacjaPraca dotyczy nierówności typu Nordhausa-Gadduma dla dominowania wypukłego.
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Lower bound on the weakly connected domination number of a tree
PublikacjaPraca dotyczy dolnego ograniczenia liczby dominowania słabo spójnego w drzewach (ograniczenie ze względu na ilość wierzchołków i ilość wierzchołków końcowych w drzewie).
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A note on the weakly convex and convex domination numbers of a torus
PublikacjaW pracy określone są liczby liczby dominowania i dominowania wypukłego torusów, czyli iloczynów kartezjańskich dwóch cykli.
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Lower bound on the distance k-domination number of a tree
PublikacjaW artykule przedstawiono dolne ograniczenie na liczbę k-dominowania w drzewach oraz scharakteryzowano wszystkie grafy ekstremalne.
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A lower bound on the total outer-independent domination number of a tree
PublikacjaA total outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V(G)D is independent. The total outer-independent domination number of a graph G, denoted by gamma_t^{oi}(G), is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every nontrivial tree T of order n with l leaves we have gamma_t^{oi}(T) >= (2n-2l+2)/3,...
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An upper bound on the 2-outer-independent domination number of a tree
PublikacjaA 2-outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)D has a at least two neighbors in D, and the set V(G)D is independent. The 2-outer-independent domination number of a graph G, denoted by gamma_2^{oi}(G), is the minimum cardinality of a 2-outer-independent dominating set of G. We prove that for every nontrivial tree T of order n with l leaves we have gamma_2^{oi}(T) <= (n+l)/2,...
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An Alternative Proof of a Lower Bound on the 2-Domination Number of a Tree
PublikacjaA 2-dominating set of a graph G is a set D of vertices of G such that every vertex not in D has a at least two neighbors in D. The 2-domination number of a graph G, denoted by gamma_2(G), is the minimum cardinality of a 2-dominating set of G. Fink and Jacobson [n-domination in graphs, Graph theory with applications to algorithms and computer science, Wiley, New York, 1985, 283-300] established the following lower bound on the 2-domination...
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Weakly convex and convex domination numbers of some products of graphs
PublikacjaIf $G=(V,E)$ is a simple connected graph and $a,b\in V$, then a shortest $(a-b)$ path is called a $(u-v)$-{\it geodesic}. A set $X\subseteq V$ is called {\it weakly convex} in $G$ if for every two vertices $a,b\in X$ exists $(a-b)$- geodesic whose all vertices belong to $X$. A set $X$ is {\it convex} in $G$ if for every $a,b\in X$ all vertices from every $(a-b)$-geodesic belong to $X$. The {\it weakly convex domination number}...
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An upper bound on the total outer-independent domination number of a tree
PublikacjaA total outer-independent dominating set of a graph G=(V(G),E(G)) is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V(G)D is independent. The total outer-independent domination number of a graph G, denoted by gamma_t^{oi}(G), is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every tree T of order n >= 4, with l leaves and s support vertices we have...
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Quantum strategies for rendezvous and domination tasks on graphs with mobile agents
PublikacjaThis paper explores the application of quantum nonlocality, a renowned and unique phenomenon acknowledged as a valuable resource. Focusing on an alternative application, we demonstrate its quantum advantage for mobile agents engaged in specific distributed tasks without communication. The research addresses the significant challenge of rendezvous on graphs and introduces a distributed task for mobile agents grounded in the graph...
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An upper bound for the double outer-independent domination number of a tree
PublikacjaA vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D, and the set V(G)\D is independent. The double outer-independent domination number of a graph G, denoted by γ_d^{oi}(G), is the minimum cardinality of a double outer-independent dominating set of G. We prove...
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A lower bound on the double outer-independent domination number of a tree
PublikacjaA vertex of a graph is said to dominate itself and all of its neighbors. A double outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D, and the set V(G)D is independent. The double outer-independent domination number of a graph G, denoted by gamma_d^{oi}(G), is the minimum cardinality of a double outer-independent dominating set of G. We...
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Nordhaus-Gaddum results for the weakly convex domination number of a graph
PublikacjaArtykuł dotyczy ograniczenia z góry i z dołu (ze względu na ilość wierzchołków) sumy i iloczynu liczb dominowania wypukłego grafu i jego dopełnienia.
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Unicyclic graphs with equal total and total outer-connected domination numbers
PublikacjaLet G = (V,E) be a graph without an isolated vertex. A set D ⊆ V (G) is a total dominating set if D is dominating and the in- duced subgraph G[D] does not contain an isolated vertex. The total domination number of G is the minimum cardinality of a total domi- nating set of G. A set D ⊆ V (G) is a total outer–connected dominating set if D is total dominating and the induced subgraph G[V (G)−D] is a connected graph. The total outer–connected...
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All graphs with paired-domination number two less than their order
PublikacjaLet G=(V,E) be a graph with no isolated vertices. A set S⊆V is a paired-dominating set of G if every vertex not in S is adjacent with some vertex in S and the subgraph induced by S contains a perfect matching. The paired-domination number γp(G) of G is defined to be the minimum cardinality of a paired-dominating set of G. Let G be a graph of order n. In [Paired-domination in graphs, Networks 32 (1998), 199-206] Haynes and Slater...
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All graphs with restrained domination number three less than their order
PublikacjaW pracy opisana jest rodzina wszystkich grafów, dla których liczbadominowania zewnętrznego jest o trzy mniejsza od ich rzędu.
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The domination of ionic conductivity in tetragonal phase of the organometal halide perovskite CH3NH3PbI3-xClx
PublikacjaOrganometal trihalide perovskites have recently gained extreme attention due to their high solar energy conversion in photovoltaic cells. Here, we investigate the contribution of iodide ions to a total conductivity of the mixed lead halide perovskite CH3NH3PbI3−xClx with a use of the modified DC Hebb–Wagner polarization method. It has been identified that an ionic conductivity dominates in tetragonal phase which is associated with room...
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Similarities and Differences Between the Vertex Cover Number and the Weakly Connected Domination Number of a Graph
PublikacjaA vertex cover of a graph G = (V, E) is a set X ⊂ V such that each edge of G is incident to at least one vertex of X. The ve cardinality of a vertex cover of G. A dominating set D ⊆ V is a weakly connected dominating set of G if the subgraph G[D]w = (N[D], Ew) weakly induced by D, is connected, where Ew is the set of all edges having at least one vertex in D. The weakly connected domination number γw(G) of G is the minimum cardinality...
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INFLUENCE OF A VERTEX REMOVING ON THE CONNECTED DOMINATION NUMBER – APPLICATION TO AD-HOC WIRELESS NETWORKS
PublikacjaA minimum connected dominating set (MCDS) can be used as virtual backbone in ad-hoc wireless networks for efficient routing and broadcasting tasks. To find the MCDS is an NP- complete problem even in unit disk graphs. Many suboptimal algorithms are reported in the literature to find the MCDS using local information instead to use global network knowledge, achieving an important reduction in complexity. Since a wireless network...
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Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs
PublikacjaGiven a graph G= (V, E), the subdivision of an edge e=uv∈E(G) means the substitution of the edge e by a vertex x and the new edges ux and xv. The domination subdivision number of a graph G is the minimum number of edges of G which must be subdivided (where each edge can be subdivided at most once) in order to increase the domination number. Also, the domination multisubdivision number of G is the minimum number of subdivisions...
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Some variants of perfect graphs related to the matching number, the vertex cover and the weakly connected domination number
PublikacjaGiven two types of graph theoretical parameters ρ and σ, we say that a graph G is (σ, ρ)- perfect if σ(H) = ρ(H) for every non-trivial connected induced subgraph H of G. In this work we characterize (γw, τ )-perfect graphs, (γw, α′)-perfect graphs, and (α′, τ )-perfect graphs, where γw(G), τ (G) and α′(G) denote the weakly connected domination number, the vertex cover number and the matching number of G, respectively. Moreover,...
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Joanna Raczek dr inż.
OsobyWykształcenie 1997 -- 2001 Studia inżynierskie, Wydział Fizyki Technicznej i Matematyki Stosowanej, Politechnika Gdańska. Kierunek: Matematyka, specjalność: Matematyka Stosowana. 2001 -- 2003 Studia magisterskie, Wydział Fizyki Technicznej i Matematyki Stosowanej, Politechnika Gdańska. Kierunek: Matematyka, specjalność: Matematyka Stosowana. 2000 -- 2004 Studia inżynierskie, Wydział Elektroniki, Informatyki i Telekomunikacji,...
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Kacper Wereszko mgr inż.
OsobyKacper Wereszko uzyskał tytuł zawodowy magistra inżyniera w 2016 roku (kierunek: informatyka, specjalność: algorytmy i technologie internetowe), a od 2017 roku jest uczestnikiem studiów doktoranckich z dyscypliny Informatyka. Obecnie pracuje jako asystent w Katedrze Algorytmów i Modelowania Systemów. Jego zainteresowania badawcze obejmują badanie własności bezpieczeństwa w grafach, problemy dominowania w grafach oraz ich praktyczne...
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Bondage number of grid graphs
PublikacjaThe bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater than the domination number of G. Here we study the bondage number of some grid-like graphs. In this sense, we obtain some bounds or exact values of the bondage number of some strong product and direct product of two paths.
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On proper (1,2)‐dominating sets in graphs
PublikacjaIn 2008, Hedetniemi et al. introduced the concept of (1,)-domination and obtained some interesting results for (1,2) -domination. Obviously every (1,1) -dominating set of a graph (known as 2-dominating set) is (1,2) -dominating; to distinguish these concepts, we define a proper (1,2) -dominating set of a graph as follows: a subset is a proper (1,2) -dominating set of a graph if is (1,2) -dominating and it is not a (1,1) -dominating...
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Super Dominating Sets in Graphs
PublikacjaIn this paper some results on the super domination number are obtained. We prove that if T is a tree with at least three vertices, then n2≤γsp(T)≤n−s, where s is the number of support vertices in T and we characterize the extremal trees.
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Valence state of Manganium in a MnCoO ceramics
Dane BadawczeManganium -cobalt based ceramics materials were produced by solid state reaction and sintred in a furnance in air atmosphere for 20h. Annealing temperature was 600 Celsius degree. For investigations a series of samples, with a various composition was chosen: MnCoO, Mn, Co2O and Mn2CoO. In order to determine valence states of the Mn, X-Ray photoemission...
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Non-isolating bondage in graphs
PublikacjaA dominating set of a graph $G = (V,E)$ is a set $D$ of vertices of $G$ such that every vertex of $V(G) \setminus D$ has a neighbor in $D$. The domination number of a graph $G$, denoted by $\gamma(G)$, is the minimum cardinality of a dominating set of $G$. The non-isolating bondage number of $G$, denoted by $b'(G)$, is the minimum cardinality among all sets of edges $E' \subseteq E$ such that $\delta(G-E') \ge 1$ and $\gamma(G-E')...
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Restrained differential of a graph
PublikacjaGiven a graph $G=(V(G), E(G))$ and a vertex $v\in V(G)$, the {open neighbourhood} of $v$ is defined to be $N(v)=\{u\in V(G) :\, uv\in E(G)\}$. The {external neighbourhood} of a set $S\subseteq V(G)$ is defined as $S_e=\left(\cup_{v\in S}N(v)\right)\setminus S$, while the \emph{restrained external neighbourhood} of $S$ is defined as $S_r=\{v\in S_e : N(v)\cap S_e\neq \varnothing\}$. The restrained differential of a graph $G$ is...
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Preface of guest editors
PublikacjaA special issue of Discussiones Mathematice Graph Theory (DMGT) is dedicated to selected papers presented at the 12th Workshop on Graph Theory: Colourings, Independence and Domination (CID) held on 16-21 September 2007 in Karpacz, Poland. It continues a series of international workshops: 1993-1997 in Lubiatów, 1998-2001 in Gronów, 2003 and 2005 in Karpacz. About 70 participants formed the audience of six invited lectures and 68...
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Some variations of perfect graphs
PublikacjaWe consider (ψk−γk−1)-perfect graphs, i.e., graphs G for which ψk(H) =γk−1(H) for any induced subgraph H of G, where ψk and γk−1 are the k -path vertex cover number and the distance (k−1)-domination number, respectively. We study (ψk−γk−1)-perfect paths, cycles and complete graphs for k≥2. Moreover, we provide a complete characterisation of (ψ2−γ1)-perfect graphs describing the set of its forbidden induced subgraphs and providing...
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Public spaces connecting cities. Green and Blue Infrastructures potential.
PublikacjaA city fragmentation causes a lot of negative effects in urban environment such as: disconnecting the environmental, functional and compositional relations, a loss of urban compactness, chaotic development, visual chaos, a domination of technical landscape, reduction of security. This is why one of main challenges for urban planners is to connect the fragmented structures by creating friendly, attractive and safe public space....
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Preface
PublikacjaThis special issue of Discussiones Mathematice Graph Theory (DMGT) is dedicated to selected papers presented at the 13th Workshop on Graph Theory: Colourings, Independence and Domination (CID) held on 18-23 September 2009 in Szklarska Poręba, Poland. It continues a series of international workshops: 1993-1997 in Lubiatów, 1998-2001 in Gronów, and 2003-2007 in Karpacz. The meeting was organized by the Faculty of Mathematics, Computer...
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Numerical modeling of exciton impact in two crystalographic phases of the organo-lead halide perovskite (CH3NH3PbI3) solar cell
PublikacjaTo improve the power conversion efficiency of solar cells based on organo–lead halide perovskites, a detailed understanding of the device physics is fundamental. Here, a computational analysis of excitons impact is reported for these types of photocell. Numerical calculations based on the model, which take into account electronic charge carriers (electrons and holes), excitons and ions, have been carried out. The role of excitons...
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2-bondage in graphs
PublikacjaA 2-dominating set of a graph G=(V,E) is a set D of vertices of G such that every vertex of V(G)D has at least two neighbors in D. The 2-domination number of a graph G, denoted by gamma_2(G), is the minimum cardinality of a 2-dominating set of G. The 2-bondage number of G, denoted by b_2(G), is the minimum cardinality among all sets of edges E' subseteq E such that gamma_2(G-E') > gamma_2(G). If for every E' subseteq E we have...
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Activation of peroxymonosulfate using carbon black nano-spheres/calcium alginate hydrogel matrix for degradation of acetaminophen: Fe3O4 co-immobilization and microbial community response
PublikacjaHerein, we focused on the degradation of acetaminophen (ACT) drug in liquid phase by peroxymonosulfate (PMS) activated by carbon black nano-spheres (CBNS). The nanostructured activator was immobilized into calcium alginate hydrogel matrix (CAHM) to avoid the washout of the fine nanostructures. The Langmuir modeling showed an insignificant contribution to the adsorption process in the removal of ACT. The basic pH conditions favored...
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Pressure drop and heat transfer during boiling and condensation at subcritical region
PublikacjaMost of the data presented in the literature relate to saturation temperatures in the range - 20°C to 40°C due to the application in refrigeration technology. There is necessity to extend databases to higher values of saturation temperature due to new applications such as Organic Rankine Cycle and high temperature heat pumps. Only few papers contain data for high reduced pressure for low boiling point liquids. This paper focus...
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Common Independence in Graphs
PublikacjaAbstract: The cardinality of a largest independent set of G, denoted by α(G), is called the independence number of G. The independent domination number i(G) of a graph G is the cardinality of a smallest independent dominating set of G. We introduce the concept of the common independence number of a graph G, denoted by αc(G), as the greatest integer r such that every vertex of G belongs to some independent subset X of VG with |X|...
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Current status and future success of renewable energy in Pakistan
PublikacjaMismatch between energy demand and supply from last two decades has been increasing because of the domination of expensive imported oil in energy mix of Pakistan. To import crude oil Government paid US $ 9 billion in 2008–2009 to meet the energy demands...
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On the double bondage in graphs
PublikacjaA vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G=(V,E) is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G, denoted by gamma_d(G), is the minimum cardinality of a double dominating set of G. The double bondage number of G, denoted by b_d(G), is the minimum cardinality among all sets...
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Non-isolating 2-bondage in graphs
PublikacjaA 2-dominating set of a graph G=(V,E) is a set D of vertices of G such that every vertex of V(G)D has at least two neighbors in D. The 2-domination number of a graph G, denoted by gamma_2(G), is the minimum cardinality of a 2-dominating set of G. The non-isolating 2-bondage number of G, denoted by b_2'(G), is the minimum cardinality among all sets of edges E' subseteq E such that delta(G-E') >= 1 and gamma_2(G-E') > gamma_2(G)....
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Unexpected Z/E isomerism of N-methyl-O-phosphothioyl benzohydroxamic acids, their oxyphilic reactivity and inertness to amines
PublikacjaThiophosphinoylation of N-methyl p-substituted benzohydroxamic acids using disulfanes (method A) or diphenylphosphinothioyl chloride (method B) provides only one conformer of the respective O-phosphothioyl derivative (Xray and NMR analysis). Undergoing the P-transamidoxylation reaction is an evidence of the reversibility of thiophosphinoylation. Only those products containing strong EWG substituents in the aroyl residue or bulky...
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Mutual Interaction between Temperature and DO Set Point on AOB and NOB Activity during Shortcut Nitrification in a Sequencing Batch Reactor in Terms of Energy Consumption Optimization
PublikacjaRecently, many wastewater treatment plants (WWTPs) have had to deal with serious problems related to the restrictive requirements regarding the euent quality, as well as significant energy consumption associated with it. In this situation, mainstream deammonification and/or shortened nitrification-denitrification via nitrite (so-called “nitrite shunt”) is a new promising strategy. This study shows the mechanisms and operating conditions...
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The Urban Mentoring as a New Method of Participatory Urban Planning in Poland
PublikacjaTwenty-five years after the return of democracy and the beginning of basing the country's economy on neoliberal developmental paradigm, Poland adopted the regulations regarding management of urban policy, which had been wait for over a decade (accession to the EU). The National Urban Policy as well as the Act on revitalization have defined, in a modern manner, the field of cooperation between the local government, the administration...