One point union of edge vertex prime graphs

  • M. Simaringa Post Graduate and Research Department of Mathematics, Thiru Kolanjiappar Government Arts College, Virudhachalam-606001, Tamil Nadu, India
  • S. Muthukumaran Siga college of Management and Computer Science, Villupuram-605601, Tamil Nadu, India.


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 $J_{m,n}^l$ $B_{3,n}\hat{O}B_{3,n}$