Square Difference 3-Equitable Labeling of Some Graphs

A square difference 3-equitable labeling of a graph G with vertex set V is a bijection f from V tof1;2;:::;j Vjg such that if each edge uv is assigned the label -1 ifj[f (u)] 2 [f (v)] 2 j 1(mod4), the label 0 ifj[f (u)] 2 [f (v)] 2 j 0(mod4) and the label 1 ifj[f (u)] 2 [f (v)] 2 j 1(mod4), then the number of edges labeled with i and the number of edges labeled 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 middle graph of paths, fan graphs, (P2n;S1), mK3, triangular snake graphs and friendship graphs.