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Let G = (V, E) be a graph. A set D ⊆ V is a total restrained dominating set of G if every vertex in V has a neighbor in D and every vertex in V − D has a neighbor in V − D. The cardinality of a minimum total restrained dominating set in G is the total restrained domination number of G. In this paper, we define the concept of total restrained domination edge… (More)

Let G be a graph with vertex set V. A set D ⊆ V is a total restrained dominating set of G if every vertex in V has a neighbor in D and every vertex in V \ D has a neighbor in V \ D. The minimum cardinality of a total restrained dominating set of G is called the total restrained domination number of G, and is denoted by γ tr (G). In this paper, we prove that… (More)

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