University of TehranJournal of Algorithms and Computation2476-277653120210601Pair Difference Cordiality of Some Snake and Butterfly Graphs1491638164910.22059/jac.2021.81649ENRPonrajDepartment of Mathematics
Sri Parakalyani College
Alwarkurichi -627 412, IndiaAGayathriResearch Scholor,Reg.No:20124012092023
Department of Mathematics
Manonmaniam Sundaranar University,
Abhishekapati,Tirunelveli–627 012, IndiaSSomasundaramDepartment of Mathematics
Manonmaniam sundarnar university, Abishekapatti, Tirunelveli-627012,
Tamilnadu, IndiaJournal Article20210602noindent Let $G = (V, E)$ be a $(p,q)$ graph.\<br />Define begin{equation*}<br />rho =<br />begin{cases}<br />frac{p}{2} ,& text{if $p$ is even}\<br />frac{p-1}{2} ,& text{if $p$ is odd}\<br />end{cases}<br />end{equation*}\ <br /> and $L = {pm1 ,pm2, pm3 , cdots ,pmrho}$ called the set of labels.\<br />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