Cubic Symmetric Graphs of Order \(4p^3\)

Abstract

A graph is said to be symmetric if its automorphism group acts transitively on its arcs. Let \(p\) be a prime. In [J. Combin. Theory B \(97 (2007) 627-646]\), Feng and Kwak classified connected cubic symmetric graphs of order \(4p\) or \(4p^2\). In this article, all connected cubic symmetric graphs of order \(4p^2\) are classified. It is shown that up to isomorphism there is one and only one connected cubic symmetric graph of order \(4p^3\) for each prime \(p\), and all such graphs are normal Cayley graphs on some groups.