## DEGREE EQUIVALENCE GRAPH OF A GRAPH

## DEGREE EQUIVALENCE GRAPH OF A GRAPH

*R. Rajendra, P. S. K. Reddy, K. V. Madhusudhan*

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## Abstract

Given a set S and an equivalence relation R on S, one can dene an equivalence graph with vertex set S. Given a graph with vertex set V , we can dene 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.

## Keywords

Equivalence relation, graph, energy of a graph.