Divisor Cordial Labeling for Vertex Switching and Duplication of Special Graphs

Abstract

A divisor cordial labeling of a graph $G$ with vertex set $V$ is a bijection $f$ from $ V $ to $\{1,2,\ldots,| V |\}$ such that an edge $e = uv$ is assigned label 1 if $f(u) | f(v)$ or $f(v) | f(u)$ and label 0 otherwise, then $|e_f(0)-e_f(1)| \leq 1$. A graph which admits divisor cordial labeling is called divisor cordial graph. In this paper we prove that vertex switching of gear graph, shell graph, flower graph are divisor cordial. We also prove some result on divisor cordial labeling for the graphs resulted from the duplication of graph elements.