3-Equitable Labeling in Context of Ring Sum of Graphs

Abstract

A function f from vertex set V of a graph G to the set {0, 1, 2} is called 3-equitable labeling if the edge labels produced by absolute difference of the labels of end vertices of the respective edges in such a way that the number of edges with label i and j differ by atmost 1 and similarly the number of vertices with label i and j differby atmost 1, {0<= i, j <= 2,  i  is not equal to j. A graph which admits 3-equitable labeling is called 3-equitable graph. Inthis paper we have derived 3-equitable labeling of ringsum of different graphs.