Total restrained domination in trees |
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Authors: | Johannes H Hattingh Andrew R Plummer |
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Institution: | a Department of Mathematics and Statistics, University Plaza, Georgia State University, Atlanta, GA 30303, USA b Department of Mathematics, University of Johannesburg, P.O. Box 524, Auckland Park, 2006 South Africa |
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Abstract: | Let G=(V,E) be a graph. A set S⊆V is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex of V-S is adjacent to a vertex in V-S. The total restrained domination number of G, denoted by γtr(G), is the smallest cardinality of a total restrained dominating set of G. We show that if T is a tree of order n, then . Moreover, we show that if T is a tree of order , then . We then constructively characterize the extremal trees T of order n achieving these lower bounds. |
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Keywords: | Total restrained domination Trees |
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