Abstract
A graph is said to be a bi-Cayley graph over a group H if it admits H as a semiregular automorphism group with two vertex-orbits. A bi-dicirculant is a bi-Cayley graph over a dicyclic group. In this paper, a classification of connected cubic bi-dicirculants is given. As byproducts, we show that every connected cubic vertex-transitive bi-dicirculant is Cayley, and up to isomorphism, there are two connected cubic edge-transitive bi-dicirculants, of which one has order 16, and the other has order 24.
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