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Chapter
Connected Domination
A set S of vertices of a connected graph G = (V, E) is a connected dominating set of G if every vertex of V − S is adjacent to at least one vertex of S and the subgraph induced by S is connected. In this chapter,...
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Article
k-Domination and k-Independence in Graphs: A Survey
In 1985, Fink and Jacobson gave a generalization of the concepts of domination and independence in graphs. For a positive integer k, a subset S of vertices in a graph G = (V, E) is k-dominating if every vertex of...
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Article
Bounding the total domination subdivision number of a graph in terms of its order
The total domination subdivision number \(\mathrm{sd}_{\gamma _{t}}(G)\) of a graph G is the m...
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Chapter
Ratios of Some Domination Parameters in Graphs and Claw-free Graphs
In the class of all graphs and the class of claw-free graphs, we give exact bounds on all the ratios of two graph parameters among the domination number, the total domination number, the paired domination numb...
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Article
Paired-Domination in Claw-Free Cubic Graphs
A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S and if the subgraph induced by S contains a perfect matching. The minimum cardinality of a pai...
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Article
(3,k)-Factor-Critical Graphs and Toughness
A graph is (r,k)-factor-critical if the removal of any set of k vertices results in a graph with an r-factor (i.e. an r-regular spanning subgraph). Let t(G) denote the toughness of graph G. In this paper, we sho...
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Article
(2,k)-Factor-Critical Graphs and Toughness
A graph is (r,k)-factor-critical if the removal of any set of k vertices results in a graph with an r-factor (i.e. with an r-regular spanning subgraph). We show that every τ-tough graph of order n with τ≥2 is (2...
