Edge vertex prime labeling of some graphs

Edge vertex prime labeling of some graphs

**Authors : **

M Simaringa^{ 1 *} and S Muthukumaran^{2}

**Author Address : **

^{1} Department of Mathematics, Thiru Kolanjiappar Govt. Arts College, Virudhachalam-606 001, Tamilnadu, India.

^{2} Department of Mathematics, Siga College of Management and Computer Science, Villupuram-605 601, Tamilnadu, India.

*Corresponding author.

**Abstract : **

Let $G=(V(G), E(G))$ be a graph with $p$ vertices and $q$ edges. A bijective function $f:V(G)igcup E(G) ightarrow { 1,2,3,...,p+q} $ is said to be an extit {edge vertex prime labeling}, if for any edge $ xy in E(G)$, it is satisfies that $ f(x), f(y)$ and $f(xy)$ 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 $J_{n,4}$.

**Keywords : **

Prime labeling, edge vertex prime labeling, relatively prime, triangular and rectangular book, butterfly graph.

**DOI : **

**Article Info : **

*Received : * January 24, 2019; *Accepted : * April 16, 2019.