### 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.**Published:**2022-06-27

**How to Cite this Article:**Preethi K. Pillai, J. Suresh Kumar, On square sum difference coloring of graphs, J. Math. Comput. Sci., 12 (2022), Article ID 180 Copyright © 2022 Preethi K. Pillai, J. Suresh Kumar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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