$k$-odd mean labeling of prism

Abstract

‎A $(p,q)$ graph $G$ is said to have a $k$-odd mean‎ ‎labeling $(k ge 1)$ if there exists an injection $f‎ : ‎V‎ ‎to {0‎, ‎1‎, ‎2‎, ‎ldots‎, ‎2k‎ + ‎2q‎ - ‎3}$ such that the‎ ‎induced map $f^*$ defined on $E$ by $f^*(uv) =‎ ‎leftlceil frac{f(u)+f(v)}{2}rightrceil$ is a‎ ‎bijection from $E$ to ${2k‎ - ‎1‎, ‎2k‎ + ‎1‎, ‎2k‎ + ‎3‎, ‎ldots‎, ‎2‎ ‎k‎ + ‎2q‎ - ‎3}$‎. ‎A graph that admits $k$-odd mean‎ ‎labeling is called $k$-odd mean graph‎. ‎In this paper‎, ‎we investigate $k$-odd mean labeling of prism $C_m times P_n$‎.