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Distance-transitive dihedrants
Authors:?tefko Miklavi?  Primo? Poto?nik
Institution:(1) Department of Mathematics and Computer Science, Faculty of Education, University of Primorska, Cankarjeva 5, 6000 Koper, Slovenia;(2) Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia
Abstract:The main result of this article is a classification of distance-transitive Cayley graphs on dihedral groups. We show that a Cayley graph X on a dihedral group is distance-transitive if and only if X is isomorphic to one of the following graphs: the complete graph K 2n ; a complete multipartite graph K t×m with t anticliques of size m, where t m is even; the complete bipartite graph without 1-factor K n,n nK 2; the cycle C 2n ; the incidence or the non-incidence graph of the projective geometry PG d-1(d,q), d ≥ 2; the incidence or the non-incidence graph of a symmetric design on 11 vertices.
Keywords:Cayley graph  Distance-regular graph  Distance-transitive graph  Dihedrant  Dihedral group  Difference set
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