On (1, 2) - Domination of Certain Graphs

Abstract

A vertex subset S of a graph G = (V,E) is called a (1,2)-dominating set if S is having the property that for every vertex v in V- S there is atleast one vertex in S of distance 1 from v and a vertex in S at a distance atmost 2 from v. The minimum cardinality of a (1, 2)-dominating set of G, denoted by ϒ (1, 2)(G), is called the (1, 2)-domination number of G. In this paper we discuss about the (1, 2)-dominating set of Shell graph C(n,n-3,), Jewel graph Jn and Comb graph Pn ʘ K1.