Square sum labeling in context of some graph operations

**MLA Style: **Mitesh J. Patel, G. V. Ghodasara "Square sum labeling in context of some graph operations" International Journal of Mathematics Trends and Technology 66.12 (2020):134-147.

**APA Style: **Mitesh J. Patel, G. V. Ghodasara(2020). Square sum labeling in context of some graph operations International Journal of Mathematics Trends and Technology, 134-147.

**Abstract**

A graph G = (V,E) with order p and size q is said to be square sum graph, if there exists a bijection mapping f : V(G)->{0,1,2,...,p-1} such that the induced function f* : E(G)->N defined by f*(uv)=(f(u))^{2}+f(v))^{2}, for every uv ε E(G) is injective. In this paper we prove that the graph obtained by joining two copies of a specific graph by a path of arbitrary length admits a square sum labeling. We also discuss here some square sum graphs in the context of arbitrary super subdivision.

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**Keywords : **Square sum graph, Arbitrary super subdivision.