A note on the <i>k</i>‐domination number of a graph

Abstract

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