3-Equitable Labeling in Context of the Barycentric Subdivision of Cycle Related Graph

A function from the vertex set of a graph G to the set {0, 1, 2} is called 3-equitable labeling if the induced edge labels are produced by the absolute difference of labels of end vertices such that the absolute difference of number of vertices of G labeled with 0, 1 and 2 differ by at most 1 and similarly the absolute difference of number of edges of G labeled with 0, 1 and 2 differ by at most 1. In this paper, we discuss 3-equitable labeling in the context of barycentric subdivision of different cycle related graphs.