Difference cordiality of product related graphs

Abstract

Let $G$ be a $\left(p,q\right)$ graph. Let $f:V\left(G\right)\to \left\{1,2,\dots ,p\right\}$ be a function. For each edge $uv$, assign the label $\left|f(u)-f(v)\right|$. $f$ is called a difference cordial labeling if $f$ is an injective map and $\left|e_{f} \left(0\right)-e_{f} \left(1\right)\right|\leq 1$ where $e_{f} \left(1\right)$ and $e_{f} \left(0\right)$ denote the number of edges labeled with $1$ and not labeled with $1$ respectively. A graph which admits a difference cordial labeling is called a difference cordial graph. In this paper, we investigate the difference cordiality of torus grids $C_{m}\times C_{n}$, $K_{m}\times P_{2}$, prism, book, mobius ladder, Mongolian tent and $n$-cube.