Abstract
A bipartite graph Γ is a bi-Cayley graph over a group H if H⩽Aut(Γ) acts faithfully and regularly on each part of Γ. In this paper, a complete classification is given of bi-quasiprimitive 2-arc-transitive bi-Cayley graphs Γ over a finite simple group G such that G is non-normal in Aut(Γ).
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