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. Marušič, 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 C2n, n⩾3;(ii)complete graphs K2n, n⩾3;(iii)complete bipartite graphs Kn,n, n⩾3;(iv)complete bipartite graphs minus a matching Kn,n−nK2, n⩾3;(v)incidence and nonincidence graphs B(H11) and B′(H11) 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 Zd-covers of Kq+1,q+1−(q+1)K2, where q⩾3 is an odd prime power and d is a divisor of and q−1, respectively, depending on whether or , 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∈PG(1,q), and the edge [i,j′] carries trivial voltage if i=∞ or j=∞, and carries voltage , the residue class of h∈Z, if and only if i−j=θh, where θ generates the multiplicative group of the Galois field Fq.