Edge vertex prime labeling of graphs

Abstract

A bijective labeling $f: V(G) \cup E(G) \rightarrow\{1,2,3, \ldots,|V(G) \cup E(G)|\}$ is an edge vertex prime labeling if for any edge $u v \in E(G)$, the numbers $f(u), f(v)$ and $f(u v)$ are pairwise relatively prime. A graph G which admits edge vertex prime labeling is called an edge vertex prime graph. In this paper, we have obtained some class of graphs such as $p+q$ is odd for $G \hat{O} W_n, G \hat{O} f_n, G \hat{O} F_n, p+q$ is even for $G \hat{O} P_n$, crown graph and union of cycles are edge vertex prime graph.