DEGREE EQUIVALENCE GRAPH OF A GRAPH

Year 2020, Volume: 10 Issue: 2, 1 - 4, 01.03.2020

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

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

Keywords

Equivalence relation, graph, energy of a graph

References

• Bapat, R. B., (2010), Graphs and matrices, Universitext, Springer.
• Harary, F., (1969), Graph theory, Addison Wesley, Reading, M. A.