Journal of Harmonized Research in Applied Science

S-PATH DOMINATION IN SHADOW DISTANCE GRAPHS

Abstract

Author(s): Vijayachandra Kumar U, R Murali

Let G = (V,E) be a simple connected and undirected graph. A subset D of V is called a dominating set of G if every vertex not in D is adjacent to some vertex in D. The domination number of G denoted b y is the minimal cardinality taken over all dominating sets of G. A dominating set of G is called a s-path dominating set of G if every path of length s in G has at least one vertex in this dominating set. We denote a s-path dominating set by . The s-path domination number of G denoted by is the minimal cardinality taken over all s - path dominating sets of G. In this paper, we determine s - path domination number of the shadow distance graph of the path graph with specified distance sets.