Let G =(V,E)be a simple undirected graph.A claw graph was one vertex pending three degree one vertex,A D graph was a triangle with two vertices that each of them pending a path of length 2.If any induced subgraph of G does not isomorphic to claw graph and not isomorphic to D graph,G was claw-free and D graph.Let S be a subset of V.If every vertex not in S was adjacent to a vertex in S,then S was a dominating set of G.If every vertex in G was adjacent to a vertex in S,then S was a total dominating set of G.The total domination number of G,was the minimum cardinality of all total dominating sets.In this paper,a tight bound for a connected claw-free and D-freegraph G withorder n were shown.
维普
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