Square Divisor Cordial Labeling in the Context of Vertex Switching

Abstract

A square divisor cordial labeling of a graph $G$ with vertex set $V(G)$ is a bijection $f$ from $V(G)$ to $\{1,2,\ldots,|V(G)|\}$ such that an edge $e=uv$ is assigned the label $1$ if $[f(u)]^2|f(v)$ or $[f(v)]^2|f(u)$ and the label $0$ otherwise, then $|e_f(0)-e_f(1)|\leq1$. A graph which admits square divisor cordial labeling is called a square divisor cordial graph. In this research article we prove that the graphs obtained by switching of a vertex in bistar, comb graph, crown and armed crown are square divisor cordial. In addition to this we also prove that the graphs obtained by switching of a vertex except apex vertex in helm and gear graph are square divisor cordial.