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A subset D of the vertex set of a graph G is a (k, p)-dominating set if every vertex v ∈ V (G) \ D is within distance k to at least p vertices in D. The parameter γ k,p (G) denotes the minimum cardinality of a (k, p)-dominating set of G. In 1994, Bean, Henning and Swart posed the conjecture that γ k,p (G) ≤ p p+k n(G) for any graph G with δ k (G) ≥ k + p −(More)
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