Total Reinforcement Number of a Graph
نویسنده
چکیده
A set D of vertices in a graph G = (V, E) is said to be a total dominating set of G if every vertex in V is adjacent to some vertex in D. The total domination number γt(G) is the minimum cardinality of a total dominating set. E(G) denotes the edge set of G, the complement of G. The minimum cardinality of a set E1 ⊂ E(G) for which γt(G+E1) < γt(G) is denoted by rt(G) and is called the total reinforcement number of G. The number rt(G) is well defined if γt(G) > 2. In this paper, we obtain some results on the total reinforcement number of a graph.
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