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  • The automorphisms of bi-Cay...
    Zhou, Jin-Xin; Feng, Yan-Quan

    Journal of combinatorial theory. Series B, January 2016, 2016-01-00, Volume: 116
    Journal Article

    A bi-Cayley graph Γ is a graph which admits a semiregular group H of automorphisms with two orbits. In this paper, the normalizer of H in the full automorphism group of Γ is determined. Applying this, a characterization of cubic edge-transitive graphs of order a 2-power is given. As byproducts, we answer a problem proposed in Godsil (1983) 16 regarding the existence of arc-regular non-normal Cayley graphs of order a 2-power, and construct the first known family of cubic semisymmetric graphs of order a 2-power.