Prime Labeling on Knödel Graphs \(W_{3,n}\)

Abstract

A graph \(G\) with vertex set \(V\) is said to have a prime labeling if its vertices can be labeled with distinct integers \(1, 2, \ldots, |V|\) such that for every edge \(xy\) in \(E(G)\), the labels assigned to \(x\) and \(y\) are relatively prime or coprime. In this paper, we show that the Knödel graph \(W_{3,n}\) is prime for \(n \leq 130\).