Neighborhood-Prime labeling for some graphs

Abstract

We consider here a graph with $n$ vertices and $m$ edges denoted by $G$ having vertex set as $V(G)$ and edge set as $E(G)$. If there is a bijective function $f$ from $V(G)$ to the set of positive integer upto $|V(G)|$ such that for every vertex $u$ with degree at least two the gcd of the labels of adjacent vertices of $u$ is 1 then $f$ is called neighborhood-prime labeling and $G$ is called neighborhood-prime graph. In the present work we constructed some particular graphs and we proved these are neighborhood-prime graphs.