On square sum difference coloring of graphs

Abstract

Let G be a graph with p vertices. A bijection f: V(G)→{0.1,2,..., p − 1} is called a Square Sum Difference (SSD) coloring of G if the induced function. f^∗: E(G)→N defined by f^∗(uv)=[f(u)]²+[f(v)]²−f(u)f(v) is injective for all edges uv∈E(G), A graph G is called an SSD colorable if G admits an SSD coloring. Further, an SSD coloring is called an odd square sum difference (OSSD) coloring, if f^∗(E) contains only odd integers. A graph G is called an OSSD colorable, if G admits an OSSD coloring.