Square Difference 3-Equitable Labeling of Paths and Cycles

A square difference 3-equitable labeling of a graph G with vertex set V is a bijection f from V to {1, 2,.... | V | } jg such that if each edge uv is assigned the label -1 if |[f (u)]2 [f (v)]2 | = -1(mod 4), the label 0 if |[f (u)]2 [f (v)]2 | = 0(mod 4) and the label 1 if |[f (u)]2 [f (v)]| = 1(mod 4), then the number of edges labeled with i and the number of edges labelled with j differ by atmost 1 for -1 = I, j = 1. If a graph has a square difference 3-equitable labeling, then it is called square difference 3-equitable graph. In this paper, we investigate the square difference 3-equitable labeling behaviour of paths and cycles.