Square sum labeling in context of some graph operations

Mitesh J. Patel; G. V. Ghodasara

doi:https://doi.org/10.14445/22315373/IJMTT-V66I12P519

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 12 | Year 2020 | Article Id. IJMTT-V66I12P519 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I12P519

Square sum labeling in context of some graph operations

Mitesh J. Patel, G. V. Ghodasara

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.

Keywords

Square sum graph, Arbitrary super subdivision.

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Citation :

Mitesh J. Patel, G. V. Ghodasara, "Square sum labeling in context of some graph operations," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 12, pp. 134-147, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I12P519