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A k−clique covering of a simple graph G, is an edge covering of G by its cliques such that each vertex is contained in at most k cliques. The smallest k for which G admits a k−clique covering is called local clique cover number of G and is denoted by lcc(G). Local clique cover number can be viewed as the local counterpart of the clique cover number which is(More)
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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