Classification of 2-arc-transitive dihedrants

A complete classification of 2-arc-transitive dihedrants, that is, Cayley graphs of dihedral groups is given, thus completing the study of these graphs initiated by the third author in [D. Marusic, On 2-arc-transitivity of Cayley graphs. J. Combin. Theory Ser. B 87 (2003) 162-196]. The list consists of the following graphs: (i) cycles C-2n.n >= 3; (ii) complete graphs K-2n. n >= 3: (iii) complete bipartite graphs K-n.n. n >= 3: (iv) complete bipartite graphs minus it matching K-n.n - nK(2), n >= 3; (v) incidence and nonincidence graphs B(H-11) and B'(H-11) of the Hadamard design on 11 points; (vi) incidence and nonincidence graphs B(PG(d, q)) and B'(PG(d, q)), with d >= 2 and q a prime power, of projective spaces; (vii) and an infinite family of regular Z(d)-covers K-q+1(2d) of Kq+ 1.q+ 1 - (q + 1) K-2, where q >= 3 is an odd prime power and d is a divisor of and q-1/2 and q - 1, respectively, depending on whether q equivalent to 1 (mod 4) or q equivalent to 3 (mod 4), obtained by identifying the vertex set of the base graph with two copies of the projective line PG(1, q), where the missing matching consists of all pairs of the form [i,i'], i epsilon PG(1. q). and the edge [i. j'] carries trivial voltage if i = infinity or j = infinity and carries voltage (h) over bar epsilon Z(d), the residue class of h epsilon Z, if and only if i - j = 0(h), where 0 generates the multiplicative group F-q* of the Galois field F-q. (c) 2008 Elsevier Inc. All rights reserved.