ENRESDOWEDNESS OF TYPE – I UNICYCLIC GRAPHS

Abstract

Let G = (V, E) be a non empty, finite, simple graph. A dominating set of a graph G containing a minimum dominating set of G is called a - endowed dominating set of G. If that set is of cardinality k then it is called a k – endowed dominating set. k - enresdowed graph is one in which every restrained dominating set of cardinality k contains a minimum restrained dominating set. A unicyclic graph is a graph consisting of a single cycle. We consider a unicyclic graph of the type , where a set of all vertices of any cycle is attached by a path , t 2 . In this paper, the enresdowedness property for the unicyclic graphs with exactly one path attached to set of all the vertices of any cycle is found.