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Cubic edge-transitive graphs of order \(2^np\)

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Abstract

Let p be a prime. Cubic edge-transitive graphs of order \(2^np\) have been classified for \(1\le n\le 4\) in the literature. This paper is devoted to a general study of cubic edge-transitive graphs of order \(2^np\). We first show that every connected cubic edge-transitive graph of order \(2^np\) with \(p>7\) is an edge-transitive N-cover of a connected cubic symmetric graph \(\Lambda _{2p}\) of order 2p, where N is a 2-group such that \(N/\Phi (N)\cong {{\mathbb {Z}}}_2^d\) with either \(d\le 2\) or \(d\ge 9\). For the case when \(d\le 2\), we give a characterization of edge-transitive N-covers of \(\Lambda _{2p}\), and for the case when \(d\ge 9\), we give a classification of edge-transitive N-covers of \(\Lambda _{2p}\) when p is a Zsigmondy prime of \(|N|-1\).

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (12071023,11671030).

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Correspondence to Jin-Xin Zhou.

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Wang, X., Zhou, JX. Cubic edge-transitive graphs of order \(2^np\). J Algebr Comb 56, 153–168 (2022). https://doi.org/10.1007/s10801-021-01102-1

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