PD-Divisor Cordial Labeling of Graphs

Abstract

Let $G=(V(G),E(G))$ be a simple, finite and undirected graph of order $n$. Given a bijection $f:V(G)\rightarrow \{1,2,...,|V(G)|\}$, we associate two integers $P=f(u)f(v)$ and $D=|f(u)-f(v)|$ with every edge $uv$ in $E(G)$. The labeling $f$ induces on edge labeling $f':E(G)\rightarrow\{0,1\}$ such that for any edge $uv$ in $E(G)$, $f'(uv)=1$ if $D\mid P$ and $f'(uv)=0$ if $D \nmid\ P$. Let $e_{f'} (i)$ be the number of edges labeled with $i\in \{0,1\}$. We say $f$ is an PD-divisor labeling if $f'(uv)=1$ for all $uv\in E(G)$. Moreover, $G$ is PD-divisor if it admits an PD-divisor labeling. We say $f$ is an PD-divisor cordial labeling if $|e_{f'}(0)-e_{f'}(1)|\leq 1$. Moreover, $G$ is PD-divisor cordial if it admits an PD-divisor cordial labeling. In this paper, we are dealing in PD-divisor cordial labeling of some standard graphs.