Two-arc-transitive bicirculants

In this paper, we determine the class of finite 2-arc-transitive bicirculants. We show that a connected 2-arc-transitive bicirculant is one of the following graphs: C-2n where n >= 2, K-2n where n >= 2, K-n,K-n where n >= 3, K-n,K-n - nK(2) where n >= 4, B(PG(d - 1, q)) and B'(PG(d - 1, q)) where d >= 3 and q is a prime power, X-1(4, q) where q equivalent to 3 (mod 4) is a prime power, K-q+1(2d) where q is an odd prime power and d >= 2 dividing q-1, AT(Q)(1 + q, 2d) where d vertical bar q - 1 and d (sic) 1/2(q - 1), AT(D)(1 + q, 2d) where d vertical bar 1/2 (q - 1) and d >= 2, Gamma(d, q, r), where d >= 2, q is a prime power and r vertical bar q - 1, Petersen graph, Desargues graph, dodecahedron graph, folded 5-cube, X(2, 2), X'(3, 2), X-2(3), AT(Q)(4, 12), GP (12, 5), GP (24, 5), B(H(11)), B'(H(11)), AT(D)(4, 6) and AT(D)(5, 6). (c) 2023 Elsevier Inc. All rights reserved.