Pair Difference Cordiality of Some Snake and Butterfly Graphs

Document Type : Research Paper

Authors

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

2 Research Scholor,Reg.No:20124012092023 Department of Mathematics Manonmaniam Sundaranar University, Abhishekapati,Tirunelveli–627 012, India

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

Abstract

\noindent Let $G = (V, E)$ be a $(p,q)$ graph.\\
Define \begin{equation*}
\rho =
\begin{cases}
\frac{p}{2} ,& \text{if $p$ is even}\\
\frac{p-1}{2} ,& \text{if $p$ is odd}\\
\end{cases}
\end{equation*}\\
and $L = \{\pm1 ,\pm2, \pm3 , \cdots ,\pm\rho\}$ called the set of labels.\\
\noindent Consider a mapping $f : V \longrightarrow L$ by assigning different labels in L to the different elements of V when p is even and different labels in L to p-1 elements of V and repeating a label for the remaining one vertex when $p$ is odd.The labeling as defined above is said to be a pair difference cordial labeling if for each edge $uv$ of $G$ there exists a labeling $\left|f(u) - f(v)\right|$ such that $\left|\Delta_{f_1} - \Delta_{f_1^c}\right| \leq 1$, where $\Delta_{f_1}$ and $\Delta_{f_1^c}$ respectively denote the number of edges labeled with $1$ and number of edges not labeled with $1$. A graph $G$ for which there exists a pair difference cordial labeling is called a pair difference cordial graph. In this paper we investigate the pair difference cordial labeling behavior of some snake and butterfly graphs.

Keywords