Degree equivalence graph of a graph

Abstract

Given a set S and an equivalence relation R on S, one can define an equivalence graph with vertex set S. Given a graph with vertex set V , we can define an equivalence relation on V using the concept of degree of a vertex as follows: two vertices a and b in V are related if and only if they are of same degree. The degree equivalence graph of a graph G is the equivalence graph with vertex set V with respect to the above equivalence relation. In this paper, we study some properties of degree equivalence graph of a graph.