Results 11 to 20 of about 7,398 (287)
On weakly connected domination in graphs II
Discrete Mathematics, 2005 A dominating set D is a weakly connected dominating set of a connected graph G=(V,E) if (V,E∩(D×V)) is connected. The weakly connected domination number of G, denoted γwc(G), is min{|S||S is a weakly connected dominating set of G}. We characterize graphs
Johannes H Hattingh
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Connected domination value in graphs [PDF]
Electronic Journal of Graph Theory and Applications, 2021 In a connected graph G = (V,E), a set D ⊂ V is a connected dominating set if for every vertex v ∈ V \ D, there exists u ∈ D such that u and v are adjacent, and the subgraph〈D〉induced by D in G is connected.
Angsuman Das
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On graphs with equal domination and connected domination numbers
Discrete Mathematics, 1999 In this paper we characterize the class of trees, unicyclic graphs and cubic graphs for which the domination number is equal to the connected domination ...
J. Paulraj Joseph +3 more
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On graphs for which the connected domination number is at most the total domination number
Discrete Applied Mathematics, 2012 In this note, we give a finite forbidden subgraph characterization of the connected graphs for which any non-trivial connected induced subgraph has the property that the connected domination number is at most the total domination number. This question is
Oliver Schaudt
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Connected cototal domination number of a graph [PDF]
Transactions on Combinatorics, 2012 A dominating set $D subseteq V$ of a graph $G = (V,E)$ is said to be a connected cototal dominating set if $langle D rangle$ is connected and $langle V-D rangle neq phi$, contains no isolated vertices.
B Basavanagoud, Sunilkumar M Hosamani
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Complexity of the game connected domination problem
Theoretical Computer ScienceThe connected domination game is a variant of the domination game where the played vertices must form a connected subgraph at all stages of the game.
Iršič Chenoweth, Vesna
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Making a Dominating Set of a Graph Connected
Discussiones Mathematicae Graph Theory, 2018 Let G = (V,E) be a graph and S ⊆ V. We say that S is a dominating set of G, if each vertex in V \ S has a neighbor in S. Moreover, we say that S is a connected (respectively, 2-edge connected or 2-connected) dominating set of G if G[S] is connected ...
Li Hengzhe, Wu Baoyindureng, Yang Weihua
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On weakly connected domination in graphs
Discrete Mathematics, 1997 A weakly connected dominating set for a connected graph is a dominating set D of vertices of the graph such that the edges not incident to any vertex in D do not separate the graph.
Hattingh, Johannes H. +4 more
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Connected Domination Stable Graphs Upon Edge Addition
Quaestiones Mathematicae, 2015 A set S of vertices in a graph G is a connected dominating set of G if S dominates G and the subgraph induced by S is connected.
Teresa W Haynes
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Connected Domination in Plane Triangulations
Involve, a Journal of MathematicsA set of vertices of a graph $G$ such that each vertex of $G$ is either in the set or is adjacent to a vertex in the set is called a dominating set of $G$.
Pavelescu, Elena, Bryant, Felicity
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