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Search results for: defensive sets in graphs
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Global defensive sets in graphs
PublicationIn the paper we study a new problem of finding a minimum global defensive set in a graph which is a generalization of the global alliance problem. For a given graph G and a subset S of a vertex set of G, we define for every subset X of S the predicate SEC ( X ) = true if and only if | N [ X ] ∩ S | ≥ | N [ X ] \ S | holds, where N [ X ] is a closed neighbourhood of X in graph G. A set S is a defensive alliance if and only if for...
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Cops, a fast robber and defensive domination on interval graphs
PublicationThe 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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Super Dominating Sets in Graphs
PublicationIn 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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On proper (1,2)‐dominating sets in graphs
PublicationIn 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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Musical Metadata Retrieval with Flow Graphs, in Rough Sets and Current Trends in Computing.
PublicationW pracy opisano metody wyszukiwania muzyki w Internecie w oparciu o opis semantyczny. W eksperymentach wykorzystano opis muzyczny stosowany w bazie CDDB. Zaprezentowano metodę grafów przepływowych zaproponowaną przez Pawlaka.
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Modele i algorytmy dla grafowych struktur defensywnych
PublicationW niniejszej pracy przeprowadzono analizę złożoności istnienia struktur defensywnych oraz równowag strategicznych w grafach. W przypadku struktur defensywnych badano modele koalicji defensywnych, zbiorów defensywnych i koalicji krawędziowych – każdy z nich w wersji globalnej, tj. z wymogiem dominacji całego grafu. W przypadku modeli równowagi strategicznej badano równowagę strategiczną koalicji defensywnych, równowagę strategiczną...
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Global defensive secure structures
PublicationLet S ⊂ V (G) for a given simple non-empty graph G. We define for any nonempty subset X of S the predicate SECG,S(X) = true iff |NG[X]∩S| ≥ |NG[X]\S|. Let H be a non-empty family of graphs such that for each vertex v ∈ V (G) there is a subgraph H of G containing v and isomorphic to a member of H. We introduce the concept of H-alliance extending the concept of global defensive secure structures. By an H-alliance in a graph G we...
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Global edge alliances in graphs
PublicationIn the paper we introduce and study a new problem of finding a minimum global edge alliance in a graph which is related to the global defensive alliance (Haynes et al., 2013; Hedetniemi, 2004) and the global defensive set (Lewoń et al., 2016). We proved the NP-completeness of the global edge alliance problem for subcubic graphs and we constructed polynomial time algorithms for trees. We found the exact values of the size of the...
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Reconfiguring Minimum Dominating Sets in Trees
PublicationWe provide tight bounds on the diameter of γ-graphs, which are reconfiguration graphs of the minimum dominating sets of a graph G. In particular, we prove that for any tree T of order n ≥ 3, the diameter of its γ-graph is at most n/2 in the single vertex replacement adjacency model, whereas in the slide adjacency model, it is at most 2(n − 1)/3. Our proof is constructive, leading to a simple linear-time algorithm for determining...
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Eqiuitable coloring of corona products of cubic graphs is harder than ordinary coloring
PublicationA graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the number of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G. In this paper the problem of determinig the equitable coloring number for coronas of cubic graphs is studied. Although the problem of ordinary coloring of coronas...
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Recurrence times in the Morse sets for a two-dimensional discrete neuron model (low resolution)
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper “Topological-numerical analysis of a two-dimensional discrete neuron model” by Paweł Pilarczyk, Justyna Signerska-Rynkowska and Grzegorz Graff. A preprint of this paper is available at https://doi.org/10.48550/arXiv.2209.03443.
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Strategic balance in graphs
PublicationFor a given graph G, a nonempty subset S contained in V ( G ) is an alliance iff for each vertex v ∈ S there are at least as many vertices from the closed neighbourhood of v in S as in V ( G ) − S. An alliance is global if it is also a dominating set of G. The alliance partition number of G was defined in Hedetniemi et al. (2004) to be the maximum number of sets in a partition of V ( G ) such that each set is an alliance. Similarly,...
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On the super domination number of lexicographic product graphs
PublicationThe 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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Dynamic F-free Coloring of Graphs
PublicationA problem of graph F-free coloring consists in partitioning the vertex set of a graph such that none of the resulting sets induces a graph containing a fixed graph F as an induced subgraph. In this paper we consider dynamic F-free coloring in which, similarly as in online coloring, the graph to be colored is not known in advance; it is gradually revealed to the coloring algorithm that has to color each vertex upon request as well...
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Double bondage in graphs
PublicationA 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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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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Polynomial Algorithm for Minimal (1,2)-Dominating Set in Networks
PublicationDominating sets find application in a variety of networks. A subset of nodes D is a (1,2)-dominating set in a graph G=(V,E) if every node not in D is adjacent to a node in D and is also at most a distance of 2 to another node from D. In networks, (1,2)-dominating sets have a higher fault tolerance and provide a higher reliability of services in case of failure. However, finding such the smallest set is NP-hard. In this paper, we...
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Morse decompositions for a two-dimensional discrete neuron model (low resolution)
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper “Topological-numerical analysis of a two-dimensional discrete neuron model” by Paweł Pilarczyk, Justyna Signerska-Rynkowska and Grzegorz Graff. A preprint of this paper is available at https://doi.org/10.48550/arXiv.2209.03443.
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Morse decompositions for a two-dimensional discrete neuron model (limited range)
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper “Topological-numerical analysis of a two-dimensional discrete neuron model” by Paweł Pilarczyk, Justyna Signerska-Rynkowska and Grzegorz Graff. A preprint of this paper is available at https://doi.org/10.48550/arXiv.2209.03443.
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Morse decompositions for a two-dimensional discrete neuron model (full range)
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper “Topological-numerical analysis of a two-dimensional discrete neuron model” by Paweł Pilarczyk, Justyna Signerska-Rynkowska and Grzegorz Graff. A preprint of this paper is available at https://doi.org/10.48550/arXiv.2209.03443.
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Computational aspects of greedy partitioning of graphs
PublicationIn this paper we consider a variant of graph partitioning consisting in partitioning the vertex set of a graph into the minimum number of sets such that each of them induces a graph in hereditary class of graphs P (the problem is also known as P-coloring). We focus on the computational complexity of several problems related to greedy partitioning. In particular, we show that given a graph G and an integer k deciding if the greedy...
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Conley-Morse graphs for a two-dimensional discrete neuron model (low resolution)
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper “Topological-numerical analysis of a two-dimensional discrete neuron model” by Paweł Pilarczyk, Justyna Signerska-Rynkowska and Grzegorz Graff. A preprint of this paper is available at https://doi.org/10.48550/arXiv.2209.03443.
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Conley-Morse graphs for a two-dimensional discrete neuron model (limited range)
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper “Topological-numerical analysis of a two-dimensional discrete neuron model” by Paweł Pilarczyk, Justyna Signerska-Rynkowska and Grzegorz Graff. A preprint of this paper is available at https://doi.org/10.48550/arXiv.2209.03443.
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Conley-Morse graphs for a two-dimensional discrete neuron model (full range)
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper “Topological-numerical analysis of a two-dimensional discrete neuron model” by Paweł Pilarczyk, Justyna Signerska-Rynkowska and Grzegorz Graff. A preprint of this paper is available at https://doi.org/10.48550/arXiv.2209.03443.
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Deterministic Rendezvous in Restricted Graphs
PublicationIn this paper we consider the problem of synchronous rendezvous in which two anonymous mobile entities (robots) A and B are expected to meet at the same time and point in a graph G = (V;E). Most of the work devoted to rendezvous in graphs assumes that robots have access to the same sets of nodes and edges, where the topology of connections may be initially known or unknown. In our work we assume the movement of robots is restricted...
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2-bondage in graphs
PublicationA 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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Application of Doubly Connected Dominating Sets to Safe Rectangular Smart Grids
PublicationSmart grids, together with the Internet of Things, are considered to be the future of the electric energy world. This is possible through a two-way communication between nodes of the grids and computer processing. It is necessary that the communication is easy and safe, and the distance between a point of demand and supply is short, to reduce the electricity loss. All these requirements should be met at the lowest possible cost....
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Conley-Morse graphs for a non-linear Leslie population model with 2 varying parameters
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "A database schema for the analysis of global dynamics of multiparameter systems" by Z. Arai, W. Kalies, H. Kokubu, K. Mischaikow, H. Oka, P. Pilarczyk, published in SIAM Journal on Applied Dynamical Systems (SIADS),...
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Conley-Morse graphs for a non-linear Leslie population model with 3 varying parameters
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "A database schema for the analysis of global dynamics of multiparameter systems" by Z. Arai, W. Kalies, H. Kokubu, K. Mischaikow, H. Oka, P. Pilarczyk, published in SIAM Journal on Applied Dynamical Systems (SIADS),...
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On Computational Aspects of Greedy Partitioning of Graphs
PublicationIn this paper we consider a problem of graph P-coloring consisting in partitioning the vertex set of a graph such that each of the resulting sets induces a graph in a given additive, hereditary class of graphs P. We focus on partitions generated by the greedy algorithm. In particular, we show that given a graph G and an integer k deciding if the greedy algorithm outputs a P-coloring with a least k colors is NP-complete for an infinite...
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Morse decompositions for a non-linear Leslie population model with 2 varying parameters
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "A database schema for the analysis of global dynamics of multiparameter systems" by Z. Arai, W. Kalies, H. Kokubu, K. Mischaikow, H. Oka, P. Pilarczyk, published in SIAM Journal on Applied Dynamical Systems (SIADS),...
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Morse decompositions for a non-linear Leslie population model with 3 varying parameters
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "A database schema for the analysis of global dynamics of multiparameter systems" by Z. Arai, W. Kalies, H. Kokubu, K. Mischaikow, H. Oka, P. Pilarczyk, published in SIAM Journal on Applied Dynamical Systems (SIADS),...
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Non-isolating bondage in graphs
PublicationA 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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Non-isolating 2-bondage in graphs
PublicationA 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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Conley-Morse graphs for a two-patch vaccination model
Open Research DataThis dataset contains selected results of rigorous numerical computations described in Section 5 of the paper "Rich bifurcation structure in a two-patch vaccination model" by D.H. Knipl, P. Pilarczyk, G. Röst, published in SIAM Journal on Applied Dynamical Systems (SIADS), Vol. 14, No. 2 (2015), pp. 980–1017, doi: 10.1137/140993934.
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Similarities and Differences Between the Vertex Cover Number and the Weakly Connected Domination Number of a Graph
PublicationA 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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Morse decompositions for a two-patch vaccination model
Open Research DataThis dataset contains selected results of rigorous numerical computations described in Section 5 of the paper "Rich bifurcation structure in a two-patch vaccination model" by D.H. Knipl, P. Pilarczyk, G. Röst, published in SIAM Journal on Applied Dynamical Systems (SIADS), Vol. 14, No. 2 (2015), pp. 980–1017, doi: 10.1137/140993934.
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Morse decompositions for a population model with harvesting. Case Ha-Se: Harvesting adults only, equal survival rates of juveniles and adults
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Morse decompositions for a population model with harvesting. Case He-S1: Equal harvesting of juveniles and adults, survival rates of juveniles and adults add up to 1
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Morse decompositions for a population model with harvesting. Case Ha-S1: Harvesting adults only, survival rates of juveniles and adults add up to 1
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Morse decompositions for a population model with harvesting. Case He-Se: Equal harvesting and equal survival rates of juveniles and adults
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Morse decompositions for a population model with harvesting. Case Hj-Se: Harvesting juveniles only, equal survival rates of juveniles and adults
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Morse decompositions for a population model with harvesting. Case Hj-S1: Harvesting juveniles only, survival rates of juveniles and adults add up to 1
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Conley-Morse graphs for a population model with harvesting. Case He-Se: Equal harvesting and equal survival rates of juveniles and adults
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Conley-Morse graphs for a population model with harvesting. Case Hj-Se: Harvesting juveniles only, equal survival rates of juveniles and adults
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Conley-Morse graphs for a population model with harvesting. Case Ha-Se: Harvesting adults only, equal survival rates of juveniles and adults
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Conley-Morse graphs for a population model with harvesting. Case Hj-S1: Harvesting juveniles only, survival rates of juveniles and adults add up to 1
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Conley-Morse graphs for a population model with harvesting. Case Ha-S1: Harvesting adults only, survival rates of juveniles and adults add up to 1
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Conley-Morse graphs for a population model with harvesting. Case He-S1: Equal harvesting of juveniles and adults, survival rates of juveniles and adults add up to 1
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "Global dynamics in a stage-structured discrete population model with harvesting" by E. Liz and P. Pilarczyk: Journal of Theoretical Biology, Vol. 297 (2012), pp. 148–165, doi: 10.1016/j.jtbi.2011.12.012.
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Continuation classes for a non-linear Leslie population model with 3 varying parameters
Open Research DataThis dataset contains selected results of rigorous numerical computations conducted in the framework of the research described in the paper "A database schema for the analysis of global dynamics of multiparameter systems" by Z. Arai, W. Kalies, H. Kokubu, K. Mischaikow, H. Oka, P. Pilarczyk, published in SIAM Journal on Applied Dynamical Systems (SIADS),...