Arc-transitive antipodal distance-regular graphs of diameter three related to PSL_d(q)

摘要

In this paper, we investigate antipodal distance-regulargraphs of diameter three and valency q(qd??1 ?? 1)=(q ?? 1) with arc-transitive automorphism group which induces an almost simple permuta-tion group on the antipodal classes with the socle isomorphic to PSLd(q);where d 3. We nd that such a graph is necessarily bipartite.