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, ngreater-or-equal, slanted3; (ii) complete graphs K2n, ngreater-or-equal, slanted3; (iii) complete bipartite graphs Kn,n, ngreater-or-equal, slanted3; (iv) complete bipartite graphs minus a matching Kn,n−nK2, ngreater-or-equal, slanted3; (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 dgreater-or-equal, slanted2 and q a prime power, of projective spaces; (vii) and an infinite family of regular View the MathML source-covers View the MathML source of Kq+1,q+1−(q+1)K2, where qgreater-or-equal, slanted3 is an odd prime power and d is a divisor of View the MathML source and q−1, respectively, depending on whether View the MathML source or View the MathML source, 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′], iset membership, variantPG(1,q), and the edge [i,j′] carries trivial voltage if i=∞ or j=∞, and carries voltage View the MathML source, the residue class of View the MathML source, if and only if i−j=θh, where θ generates the multiplicative group View the MathML source of the Galois field View the MathML source.