Prime Cordial Labeling of Flower Snark and Related Graphs

Abstract

A graph with vertex set \(V\) is said to have a prime cordial labeling if there is a bijection \(f\) from \(V\) to \(\{1,2,\ldots,|V|\}\) 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 the Flower Snark and its related graphs are prime cordial for all \(n \geq 3\).