Classifying cubic \(s\)-regular graphs of orders \(22p \) and \( 22p^{2}\)

Abstract

A graph is \(s\)-regular if its automorphism group acts regularly on the set of \(s\)-arcs. In this study, we classify the connected cubic \(s\)-regular graphs of orders \(22p \) and \( 22p^{2}\) for each \( s \geq 1 \), and each prime \(p\).