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A subset S of a vertex set of a graph G is a total (k, r)-dominating set if every vertex u ∈ V (G) is within distance k of at least r vertices in S. The minimum cardinality among all total (k, r)-dominating sets of G is called the total (k, r)-domination number of G, denoted by γ t (k,r) (G). We previously gave an upper bound on γ t (2,r) (G(n, p)) in… (More)

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