Prime labeling of Franklin graph

Abstract

A graph G = (V, E) with n vertices is said to accept prime labelling if each pair of  adjacent vertices can be labelled with different positive numbers not exceeding n, such that the label of each pair of adjacent vertices are relatively prime. Prime graph is a graph G that allows prime labelling. In this study, we look into prime labelling for a few different graph types. We focused on Franklin graph prime labelling in particular.