Neighborhood-Prime labeling for some graphs

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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 :

10.26637/MJM0701/0021

Article Info :

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

 

 

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