University Of Tehran Press Journal of Algorithms and Computation 2476-2776 53 1 2021 06 01 Pair Difference Cordiality of Some Snake and Butterfly Graphs 149 163 81649 10.22059/jac.2021.81649 EN R Ponraj Department of Mathematics Sri Parakalyani College Alwarkurichi -627 412, India A Gayathri Research Scholor,Reg.No:20124012092023 Department of Mathematics Manonmaniam Sundaranar University, Abhishekapati,Tirunelveli–627 012, India S Somasundaram Department of Mathematics Manonmaniam sundarnar university, Abishekapatti, Tirunelveli-627012, Tamilnadu, India Journal Article 2021 06 02 \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.

https://jac.ut.ac.ir/article_81649_9670058e7708586f959c57de1e3434f5.pdf