This paper classifies cubic edge-transitive graphs of order 2p^4 for primes p, indicating their symmetric properties.
A graph Γ is edge-transitive (s-arc-transitive, respectively) if its full automorphism group Aut\,(Γ) acts transitively on the set of edges (the set of s-arcs in Γ for an integer s≥ 0, respectively). A $1$-arc-transitive graph is called an arc-transitive graph or a symmetric graph. In this paper, we construct cubic symmetric bi-Cayley graphs over some groups of order p⁴, where p≥ 7 is a prime. Using these constructions, we classify the connected cubic edge-transitive graphs of order 2p⁴ for each prime p and we also show that all these graphs are symmetric.
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Wang et al. (2025) studied this question.
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