On the prime labeling of generalized petersen graph P (n, 1)

Abstract

A graph G with vertex set V is said to have a prime labeling if its vertices can be labeled with distinct integers 1,2,..., |V| such that for every edge xy in G, the labels assigned to x and y are relatively prime or coprime. A graph is called prime if it has a prime labeling. In this paper, we show that generalized Petersen graph P(n, 1) is not prime for odd n, prime for even n ≤ 2500, and conjecture that P (n, 1) is prime for all even n.