PD-prime cordial labeling of graphs

Document Type: Research Paper

Authors

1 Department of Mathematics Sri Parakalyani College Alwarkurichi -627 412, India

2 Research Scholar, Department of Mathematics Sri Paramakalyani College, Alwarkurichi-627412, Tamilnadu, India

3 Department of Mathematics Manonmaniam sundarnar university, Abishekapatti, Tirunelveli-627012, Tamilnadu, India

Abstract

\vspace{0.2cm}
Let $G$ be a graph and $f:V(G)\rightarrow \{1,2,3,.....\left|V(G)\right|\}$ be a bijection. Let $p_{uv}=f(u)f(v)$ and\\
$ d_{uv}=
\begin{cases}
\left[\frac{f(u)}{f(v)}\right] ~~if~~ f(u) \geq f(v)\\ \\
\left[\frac{f(v)}{f(u)}\right] ~~if~~ f(v) \geq f(u)\\
\end{cases}
$\\
for all edge $uv \in E(G)$. For each edge $uv$ assign the label $1$ if $gcd (p_{uv}, d_{uv})=1$ or $0$ otherwise. $f$ is called PD-prime cordial labeling if $\left|e_{f}\left(0\right)-e_{f}\left(1\right) \right| \leq 1$ where $e_{f}\left(0\right)$ and $e_{f}\left(1\right)$ respectively denote the number of edges labelled with $0$ and $1$. A graph with admit a PD-prime cordial labeling is called PD-prime cordial graph.
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Keywords