Bounds on perfect k-domination in trees: An algorithmic approach

Abstract

Let k be a positive integer and G = (V,E) be a graph. A vertex subset D of a graph G is called a perfect k-dominating set of G if every vertex v of G not in D is adjacent to exactly k vertices of D. The minimum cardinality of a perfect k-dominating set of G is the perfect k-domination number γkp(G). In this paper, a sharp bound for γ kp(T) is obtained where T is a tree.