Abstract
This work studies edge-transitive bi-circulants of order 2n with Zn being a Hall subgroup of the full automorphism groups. The automorphism groups of such graphs are completely determined. As an application, a classification is given of bipartite edge-transitive bi-circulants of order 2n with valency less than the smallest prime divisors of n. This also leads to a new construction of an infinite family of arc-regular bi-circulants.
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