On the prime cordial labeling of generalized Petersen graph

Abstract

A graph with vertex set V is said to have a prime cordial labeling if there is a bijection f from V to {1,2, ...,|V|} such that if each edge uv is assigned the label 1 for the greatest common divisor gcd(f(u), f(v)) = 1 and 0 for gcd(f(u),f(v)) > 1 then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. In this paper, we show that generalized Petersen graph P(n, k) is prime cordial for all n and k except P(4, 1).