Oblong mean prime labeling of variations of cycle, star and path

Abstract

A graph $G=(V, E)$ with $p$ vertices and $q$ edges is said to be admit oblong mean prime labeling if there exists a bijection $f: V(G) \rightarrow\{2,6,12, \ldots p(p+1)\}$ such that the induced function $f_{a m p l}^*: E(G) \rightarrow N$ given by
$$
f_{\text {ampl }}^*(u v)=\frac{f(u)+f(v)}{2} \text {, Vedges } w v \in E(G)
$$
the induced function $f_{a m p l}^*(u v)$ is said to be an oblong mean prime labeling if the god of each vertex of degree atleast 2, is one. A graph which admits oblong mean prime labeling is called oblong mean prime graph. In the paper we proved that shadow graph of even cycle, splitting graph of even cycle,square graph $P_n^2 \&$ union of two paths.