A study on distance k-domination in digraphs

Abstract

Let D = (V, A) be a finite and simple directed graph (digraph) with vertex set V and arc set A. For an integer k ≥ 1, the out k-neighborhood of a vertex ν is defined as . A set S ⊆ V is said to be a distance k-dominating set in D if N+ k (S) ∪ S = V. The minimum distance k-dominating set in D is the distance k-domination number, . For two integers s ≥ 2 and k, the (s, k) - kernal set and the (s, k) - kernal number, are studied. This parameter is also computed for different types of digraphs. Strong digraphs (SDs) are studied and of SDs are determined in terms of the radius and diameter of SDs. Also (2, k) - kernals of directed wounded spider are classified with . Some upper and lower bounds on are determined and characterized some digraphs achieving these bounds.