Edge vertex prime labeling of some graphs

Abstract

Let $G=(V(G), E(G))$ be a graph with $p$ vertices and $q$ edges. A bijective function $f: V(G) \cup E(G) \rightarrow\{1,2,3, \ldots, p+$ $q\}$ is said to be an edge vertex prime labeling, if for any edge $x y \in E(G)$, it is satisfies that $f(x), f(y)$ and $f(x y)$ are pairwise relatively prime. In this paper, we investigate several families of edge vertex prime labeling for triangular and rectangular book, Butterfly graph, Drums graph $D_n$, Jahangir graph $J_{n, 3}$ and $J_{n, 4}$.