Results 51 to 60 of about 259 (109)
Changing and Unchanging of the Domination Number of a Graph: Path Addition Numbers
Discussiones Mathematicae Graph Theory, 2021 Given a graph G =(V, E) and two its distinct vertices u and v, the (u, v)-Pk-addition graph of G is the graph Gu,v,k−2 obtained from disjoint union of G and a path Pk : x0, x1,...,xk−1, k ≥ 2, by identifying the vertices u and x0, and identifying the ...
Samodivkin Vladimir
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Independent Transversal Total Domination Versus Total Domination in Trees
Discussiones Mathematicae Graph Theory, 2021 A subset of vertices in a graph G is a total dominating set if every vertex in G is adjacent to at least one vertex in this subset. The total domination number of G is the minimum cardinality of any total dominating set in G and is denoted by γt(G).
Martínez Abel Cabrera +2 more
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Sufficient Conditions for a Digraph to Admit A (1, ≤ ℓ)-Identifying Code
Discussiones Mathematicae Graph Theory, 2021 A (1, ≤ ℓ)-identifying code in a digraph D is a subset C of vertices of D such that all distinct subsets of vertices of cardinality at most ℓ have distinct closed in-neighbourhoods within C. In this paper, we give some sufficient conditions for a digraph
Balbuena Camino +2 more
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Domination versus semipaired domination in trees
, 2021 In this paper, we study a parameter that is a relaxation of an important domination parameter, namely the paired domination. A set D of vertices in G is a semipaired dominating set of G if it is a dominating set of G ...
Zhuhang, Wei, Hao, Guoliang
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On the Lovasz O-number of Almost Regular Graphs With Application to Erdos-Renyi Graphs [PDF]
AMS classifications: 05C69; 90C35; 90C22;Erdos-Renyi graph;stability number;Lovasz O-number;Schrijver O-number;C*-algebra;semidefinite ...
Klerk, E. de +3 more
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Matching, path covers, and total forcing sets
, 2020 A dynamic coloring of the vertices of a graph G starts with an initial subset S of colored vertices, with all remaining vertices being non-colored. At each discrete time interval, a colored vertex with exactly one non-colored neighbor forces this non ...
Davila, Randy, Henning, Michael A.
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Power Domination in the Generalized Petersen Graphs
Discussiones Mathematicae Graph Theory, 2020 The problem of monitoring an electric power system by placing as few measurement devices in the system can be formulated as a power dominating set problem in graph theory.
Zhao Min, Shan Erfang, Kang Liying
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On the signed Roman k-domination in graphs
, 2020 Let k ≥ 1 be an integer and G be a simple and finite graph with vertex set V (G). A signed Roman k-dominating function (SRkDF) on a graph G is a function f : V (G) → {−1, 1, 2} such that (i) every vertex v with f(v) = −1 is adjacent to at least one ...
Amjadi, J +3 more
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Conflict-free coloring of graphs
, 2013 We study the conflict-free chromatic number χCF of graphs from ex-tremal and probabilistic point of view. We resolve a question of Pach and Tardos about the maximum conflict-free chromatic number an n-vertex graph can have. Our construction is randomized.
Tibor Szabó +2 more
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Domination Parameters of a Graph and its Complement
Discussiones Mathematicae Graph Theory, 2018 A dominating set in a graph G is a set S of vertices such that every vertex in V (G) \ S is adjacent to at least one vertex in S, and the domination number of G is the minimum cardinality of a dominating set of G.
Desormeaux Wyatt J. +2 more
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