On Legendre Cordial Labeling of Some Graphs Under Graph Opearations

Abstract

For a simple connected graph $G$ of order $n$, a bijective function $f:V(G)\to \{1,2,\cdots ,n\}$ is said to be a Legendre cordial labeling modulo $p$, where $p$ is an odd prime, if the induced function $f_p^{\ast }:E(G)\to \{0,1\}$, defined by $f_p^{\ast }(uv)=0$ whenever $([f(u)+f(v)]/p)=-1$ or $f(u)+f(v)\equiv 0(\text{mod }p)$, and $f_p^{\ast }(uv)=1$ whenever $([f(u)+f(v)]/p)=1$, satisfies the condition $|e_{f_p^{\ast }}(0)-e_{f_p^{\ast }}(1)|\le 1$ where $e_{f_p^{\ast }}(i)$ is the number of edges with label $i$ ($i=0,1$). This paper investigates the Legendre cordial labeling of graphs obtained through various operations: join, corona, lexicographic product, cartesian product, tensor product, and strong product.

This preprint is also available on Zenodo: https://doi.org/10.5281/zenodo.17112976