$k$-odd mean labeling of prism

Document Type: Research Paper

Authors

1 Periyar E.V.R. College(Autonomous)

2 Roever Engineering College

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 $f^*(uv) =‎ ‎\left\lceil \frac{f(u)+f(v)}{2}\right\rceil$ 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 $C_m \times P_n$‎.

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