One point union of edge vertex prime graphs

Abstract

Let $G(V,E)$ be a graph with $s$ vertices and $t$ edges. A bijective function $h_{1}:V(G)\bigcup E(G)\rightarrow \{ 1,2,3,...,s+t\} $ is said to be an edge vertex prime labeling, for any $xy\in E(G)$, if it satisfied that $h_{1}(x)$,$h_{1}(y)$ and $h_{1}(xy)$ are pairwise relatively prime. A graph $G$ which admits edge vertex prime labeling is called an edge vertex prime graph. In this paper, we investigate several class of one point union of graphs are edge vertex prime graphs for $B_{m,n}^l$, $CT_{m,n}^l$, $D_{m,r,n}^l$, $Y^l$-tree, Jelly fish $J_{m,n}$, Jelly fish $J_{m,n}^l$ $B_{3,n}\hat{O}B_{3,n}$