A note on the k-domination number of a graph

Abstract

The k-domination number of a graph G=G(V,E), γk(G), is the least cardinality of a set X⊂V such that any vertex in VX is adjacent to at least k vertices of X.Extending a result of Cockayne, Gamble and Shepherd [4], we prove that if δ(G)≥n+1nk−1, n≥1, k≥1 then, γk(G)≤npn+1, where p is the order of G.