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Search results for: G-QUADRUPLEXES
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On trees with double domination number equal to total domination number plus one
PublicationA 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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On the size of identifying codes in triangle-free graphs
PublicationIn an undirected graph G, a subset C⊆V(G) such that C is a dominating set of G, and each vertex in V(G) is dominated by a distinct subset of vertices from C, is called an identifying code of G. The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. For a given identifiable graph G, let gammaID(G) be the minimum cardinality of an identifying code in G. In this paper, we show that for any connected...
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Minimum order of graphs with given coloring parameters
PublicationA complete k-coloring of a graph G=(V,E) is an assignment F: V -> {1,...,k} of colors to the vertices such that no two vertices of the same color are adjacent, and the union of any two color classes contains at least one edge. Three extensively investigated graph invariants related to complete colorings are the minimum and maximum number of colors in a complete coloring (chromatic number χ(G) and achromatic number ψ(G), respectively),...
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Some Progress on Total Bondage in Graphs
PublicationThe total bondage number b_t(G) of a graph G with no isolated vertex is the cardinality of a smallest set of edges E'⊆E(G) for which (1) G−E' has no isolated vertex, and (2) γ_t(G−E')>γ_t(G). We improve some results on the total bondage number of a graph and give a constructive characterization of a certain class of trees achieving the upper bound on the total bondage number.
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A lower bound on the total outer-independent domination number of a tree
PublicationA 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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On trees with equal domination and total outer-independent domination numbers
PublicationFor 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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GreedyMAX-type Algorithms for the Maximum Independent Set Problem
PublicationA maximum independent set problem for a simple graph G = (V,E) is to find the largest subset of pairwise nonadjacent vertices. The problem is known to be NP-hard and it is also hard to approximate. Within this article we introduce a non-negative integer valued functionp defined on the vertex set V(G) and called a potential function of agraph G, while P(G) = max{vinV(G)| p(v)} is called a potential of G. For any graph P(G) <= D(G),...
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T-colorings, divisibility and circular chromatic number
PublicationLet T be a T-set, i.e., a finite set of nonnegative integers satisfying 0 ∈ T, and G be a graph. In the paper we study relations between the T-edge spans espT (G) and espd⊙T (G), where d is a positive integer and d ⊙ T = {0 ≤ t ≤ d (max T + 1): d |t ⇒ t/d ∈ T} . We show that espd⊙T (G) = d espT (G) − r, where r, 0 ≤ r ≤ d − 1, is an integer that depends on T and G. Next we focus on the case T = {0} and show that espd⊙{0} (G) =...
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An upper bound on the 2-outer-independent domination number of a tree
PublicationA 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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On trees with double domination number equal to 2-domination number plus one
PublicationA 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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Parity vertex colouring of graphs
PublicationA parity path in a vertex colouring of a graph is a path along which each colour is used an even number of times. Let Xp(G) be the least number of colours in a proper vertex colouring of G having no parity path. It is proved that for any graph G we have the following tight bounds X(G) <= Xp(G) <=|V(G)|− a(G)+1, where X(G) and a(G) are the chromatic number and the independence number of G, respectively. The bounds are improved for...
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Equitable coloring of corona products of graphs
PublicationIn this paper we consider an equitable coloring of some corona products of graphs G and H in symbols, G o H). In particular, we show that deciding the colorability of G o H is NP-complete even if G is 4-regular and H is K_2. Next, we prove exact values or upper bounds on the equitable chromatic number of G o H, where G is an equitably 3- or 4-colorable graph and H is an r-partite graph, a path, a cycle or a complete graph.
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Isolation Number versus Domination Number of Trees
PublicationIf 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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Graphs with isolation number equal to one third of the order
PublicationA set D of vertices of a graph G is isolating if the set of vertices not in D and with no neighbor in D is independent. The isolation number of G, denoted by \iota(G) , is the minimum cardinality of an isolating set of G. It is known that \iota(G) \leq n/3 , if G is a connected graph of order n, , distinct from C_5 . The main result of this work is the characterisation of unicyclic and block graphs of order n with isolating number...
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The Backbone Coloring Problem for Bipartite Backbones
PublicationLet G be a simple graph, H be its spanning subgraph and λ≥2 be an integer. By a λ -backbone coloring of G with backbone H we mean any function c that assigns positive integers to vertices of G in such a way that |c(u)−c(v)|≥1 for each edge uv∈E(G) and |c(u)−c(v)|≥λ for each edge uv∈E(H) . The λ -backbone chromatic number BBCλ(G,H) is the smallest integer k such that there exists a λ -backbone coloring c of G with backbone H satisfying...
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Review of cigars and cigar-type products as potential sources of consumer exposure to heavy metals
PublicationThe popularity of cigars, growing since 1993, has not gone hand in hand with the increased interest of researchers in these products. Although the literature widely describes the harmfulness of tobacco and the content of toxic substances in tobacco products, the topic is often treated selectively as relating primarily to cigarettes and rarely extends to other products of the broadly defined tobacco industry. However, there is no...
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An upper bound for the double outer-independent domination number of a tree
PublicationA 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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BTEX concentration levels in urban air in the area of the Tri-City agglomeration (Gdansk, Gdynia, Sopot), Poland
PublicationThe paper presents and discusses the results of atmospheric air quality research conducted in 2012 with reference to the level of BTEX compounds in the Tri-City agglomeration—Gdansk, Gdynia, and Sopot (northern Poland). At the stage of BTEX sampling from the ambient air, Radiello® diffusive passive samplers were applied. The annual time-weighted average concentrations for benzene, toluene, ethylbenzene, and xylenes (BTEX) in the...
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Impact of aeration conditions on the removal of low concentrations of nitrogen in a tertiary partially aerated biological filter
PublicationA submerged biological aerated filter (BAF) partially aerated was used to study the removal of low concentrations of ammonia nitrogen (0.3 g N/m3 to 30.5 g N/m3) typically found in nutrient enriched river and lake waters, and treated effluents. Four series of experiments were performed with a synthetic wastewater at ammonia loading rates between 6 g N/m3 d and 903 g N/m3 d and C/N ratios from 2 to 20. The results showed that ammonia...
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Progress on Roman and Weakly Connected Roman Graphs
PublicationA graph G for which γR(G)=2γ(G) is the Roman graph, and if γwcR(G)=2γwc(G), then G is the weakly connected Roman graph. In this paper, we show that the decision problem of whether a bipartite graph is Roman is a co-NP-hard problem. Next, we prove similar results for weakly connected Roman graphs. We also study Roman trees improving the result of M.A. Henning’s A characterization of Roman trees, Discuss. Math. Graph Theory 22 (2002)....
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On trees with equal 2-domination and 2-outer-independent domination numbers
PublicationFor 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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A Noether theorem for stochastic operators on Schatten classes
PublicationWe prove that a stochastic (Markov) operator S acting on a Schatten class C_1 satisfies the Noether condition S'(A) = A and S'(A^2) = A^2, where A is a Hermitian bounded linear operator on a complex Hilbert space H, if and only if, S(E(G)XE(G)) = E(G)S(X)E(G) holds true for every Borel subset G of the real line R, where E(G) denotes the orthogonal projection coming from the spectral resolution of A. Similar results are obtained...
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Teloxantron inhibits the processivity of telomerase with preferential DNA damage on telomeres
PublicationTelomerase reactivation is one of the hallmarks of cancer, which plays an important role in cellular immortalization and the development and progression of the tumor. Chemical telomerase inhibitors have been shown to trigger replicative senescence and apoptotic cell death both in vitro and in vivo. Due to its upregulation in various cancers, telomerase is considered a potential target in cancer therapy. In this study, we identified...
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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublicationConsider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...
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Interval incidence coloring of subcubic graphs
PublicationIn this paper we study the problem of interval incidence coloring of subcubic graphs. In [14] the authors proved that the interval incidence 4-coloring problem is polynomially solvable and the interval incidence 5-coloring problem is N P-complete, and they asked if χii(G) ≤ 2∆(G) holds for an arbitrary graph G. In this paper, we prove that an interval incidence 6-coloring always exists for any subcubic graph G with ∆(G) = 3.
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Coronas and Domination Subdivision Number of a Graph
PublicationIn 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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Some variants of perfect graphs related to the matching number, the vertex cover and the weakly connected domination number
PublicationGiven 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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On trees attaining an upper bound on the total domination number
PublicationA 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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Interpolation properties of domination parameters of a graph
PublicationAn 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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Restrained differential of a graph
PublicationGiven 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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The convex domination subdivision number of a graph
PublicationLet 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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A lower bound on the double outer-independent domination number of a tree
PublicationA 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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Weakly convex and convex domination numbers of some products of graphs
PublicationIf $G=(V,E)$ 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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TOTAL DOMINATION MULTISUBDIVISION NUMBER OF A GRAPH
PublicationThe 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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The emissions of monoaromatic hydrocarbons from small polymeric toys placed in chocolate food products
PublicationThe article presents findings on the emissions of selected monoaromatic hydrocarbons from children's toys placed in chocolate food products. The emission test system involved the application of a new type of microscale stationary emission chamber, μ-CTE™ 250. In order to determine the type of the applied polymer in the manufacture of the tested toys, Fourier transform infrared spectroscopy and thermogravimetric analysis coupled...
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2-outer-independent domination in graphs
PublicationWe 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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Bipartite theory of graphs: outer-independent domination
PublicationLet $G = (V,E)$ 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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Evaluation of Langmuir and Freundlich Isotherms for Removal of Cephalexin and Tetracycline Antibiotics By Sistan Sand from Water and Wastewater Samples
PublicationIn this research, Sistan sand was used as a natural and inexpensive sorbent for removal of cephalexin and tetracycline antibiotics from water and wastewater samples. For a concentration 60.0 mg L-1 of cephalexin, optimum removal conditions were: pH of the sample 3.0, adsorbent amount 1.0 g, contact time 20.0 min, added amount of sodium chloride to adjust the ionic strength of the solution 7.0 g L-1. Langmuir isotherm was the best...
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Właściwości interpolacyjne parametrów dominowania w grafach
PublicationFunkcję Pi o wartościach całkowitych nazywamy funkcją interpolującą, jeżeli dla każdego spójnego grafu G, Pi(T(G)) jest interwałem, przy czym T(G) jest zbiorem wszystkich drzew spinających grafu G. W artykule tym przedstawia się interpolacyjny charakter parametrów związanych z różnymi rodzajami dominowania.
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Optimal backbone coloring of split graphs with matching backbones
PublicationFor a graph G with a given subgraph H, the backbone coloring is defined as the mapping c: V(G) -> N+ such that |c(u)-c(v)| >= 2 for each edge uv \in E(H) and |c(u)-c(v)| >= 1 for each edge uv \in E(G). The backbone chromatic number BBC(G;H) is the smallest integer k such that there exists a backbone coloring with max c(V(G)) = k. In this paper, we present the algorithm for the backbone coloring of split graphs with matching backbone.
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Domination subdivision and domination multisubdivision numbers of graphs
PublicationThe 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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On Tradeoffs Between Width- and Fill-like Graph Parameters
PublicationIn this work we consider two two-criteria optimization problems: given an input graph, the goal is to find its interval (or chordal) supergraph that minimizes the number of edges and its clique number simultaneously. For the interval supergraph, the problem can be restated as simultaneous minimization of the path width pw(G) and the profile p(G) of the input graph G. We prove that for an arbitrary graph G and an integer t ∈ {1,...
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Confined granular flow in silos with inserts - full-scale experiments
PublicationArtykuł omawia wyniki doświadczalne przepływów silosowych w silosach w naturalnej skali ze wstawkami. Podczas doświadczeń pomierzono przemieszczenia oraz napór na ściany. Zastosowano różne typy wstawek położone na różnej wysokości. Wyniki badań doświadczalnych porównano z przepływami bez wstawek.
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Weakly convex domination subdivision number of a graph
PublicationA 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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Konkurencyjność międzynarodowa krajów
PublicationZa podstawę badań autorskich nt. konkurencyjności międzynarodowej przyjęto raporty World Economic Forum (WEF). W rozdziale pierwszym przedstawiono rozważania związane z teoretycznymi aspektami konkurencyjności międzynarodowej oraz zaproponowano autorską definicję pojęcia konkurencyjności międzynarodowej kraju. W rozdziale drugim omówiono metodologię pomiaru Global Competitiveness Index (GCI). Podjęto próbę krytycznej oceny GCI,...
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Domination-Related Parameters in Rooted Product Graphs
PublicationAbstract 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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Clarke duality for Hamiltonian systems with nonstandard growth
PublicationWe consider the existence of periodic solutions to Hamiltonian systems with growth conditions involving G-function. We introduce the notion of symplectic G-function and provide relation for the growth of Hamiltonian in terms of certain constant CG associated to symplectic G-function G. We discuss an optimality of this constant for some special cases. We also provide applications to the Φ-laplacian type systems.
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Conversion of waste biomass to designed and tailored activated chars with valuable properties for adsorption and electrochemical applications
PublicationWaste biomass, a renewable energy source, is inexpensive material that has great potential in sorp-tion and electrochemical application. The selected waste materials (corncobs, coconut shells, wal-nuts, and pistachio husks) allow to close the production cycle and enable material recycling, which are important aspects in the hierarchy of waste management. The proposed methodology for pro-duction and activation of biochars can be...
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Electrochemical Characterization of Gelatine Derived Ceramics
PublicationNew materials obtained by pyrolysis of gelatine (G) and poly(1,2-dimethylsilazane) (PSN) (weight ratio: G/PSN 70/30) at temperatures 700 and 900 °C were characterized by SEM and Raman spectroscopy. The presence of ceramics influences on the cluster size of the materials. Electrochemical tests were performed by cyclic voltammetry and galvanostatic cyclic polarization. The capacity of G/PSN was 464 and 527 mAh/g for materials pyrolysed...
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Weakly connected Roman domination in graphs
PublicationA 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...