Neighborhood-Prime labeling for some graphs

Neighborhood-Prime labeling for some graphs

**Authors : **

N.P. Shrimali^{ 1} , A.K. Rathod ^{2 *} and P.L. Vihol ^{3}

**Author Address : **

^{1} Department of Mathematics, Gujarat University, Ahmedabad, India.

^{2,3 }Department of Mathematics, Government Engineering College, Sector-28, Gandhinagar, India.

*Corresponding author.

**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.

**Keywords : **

Neighborhood of a vertex, neighborhood-prime labeling.

**DOI : **

**Article Info : **

*Received : * August 22, 2018; *Accepted : * January 17, 2019.