Total restrained domination in trees

نویسندگان

  • Johannes H. Hattingh
  • Elizabeth Jonck
  • Ernst J. Joubert
  • Andrew R. Plummer
چکیده

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 γtr(T ) ≥ d(n + 2)/2e. Moreover, we show that if T is a tree of order n ≡ 0 mod 4, then γtr(T ) ≥ d 2 e + 1. We then constructively characterize the extremal trees T of order n achieving these lower bounds.

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عنوان ژورنال:
  • Discrete Mathematics

دوره 307  شماره 

صفحات  -

تاریخ انتشار 2007