Total domination supercritical graphs with respect to relative complements
نویسندگان
چکیده
منابع مشابه
Total domination supercritical graphs with respect to relative complements
A set S of vertices of a graph G is a total dominating set if every vertex of V (G) is adjacent to some vertex in S. The total domination number t(G) is the minimum cardinality of a total dominating set of G. Let G be a connected spanning subgraph of Ks;s, and let H be the complement of G relative to Ks;s; that is, Ks;s = G ⊕ H is a factorization of Ks;s. The graph G is k-supercritical relative...
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A total dominating set of a graph G is a set S of vertices of G such that every vertex is adjacent to a vertex in S. The total domination number of G, denoted by γt(G), is the minimum cardinality of a total dominating set. Let G be a connected spanning subgraph of Ks,s and letH be the complement of G relative to Ks,s; that is, Ks,s = G⊕H . The graph G is k-supercritical relative to Ks,s if γt(G...
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We show that the total domination number of a graph G whose complement , G c , does not contain K3;3 is at most (G c), except for complements of complete graphs, and graphs belonging to a certain family which is characterized. In the case where G c does not contain K4;4 we show that there are four exceptional families of graphs, and determine the total domination number of the graphs in each one.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(02)00537-x