On 0-Edge Magic Labeling of Some Graphs

Abstract

A graph $G = (V,E)$ where $ V = \left\{v_i, 1 \leq i \leq n \right\} $ and $ E = \left\{v_iv_{i+1}, 1 \leq i \leq n \right\} $ is 0-edge magic if there exists a bijection $f: V(G) \rightarrow \left\{1,-1\right\}$ then the induced edge labeling $ f : E\rightarrow \left\{ 0 \right\} $, such that for all $uv$ $\in$ $E(G)$, $f^*(uv)$ = $ f(u) + f(v) = 0 $. A graph $G$ is called \textit{0-edge magic} if there exists a 0-edge magic labeling of $G$. In this paper, we determine the 0-edge magic labeling of the cartesian graphs $P_m \times P_n$ and $C_m \times C_n$, and the generalized Petersen graph $P(m,n)$.