DISTANCE REGULAR COVERS OF THE COMPLETE GRAPH

Distance regular graphs fall into three families: primitive, antipodal, and bipartite. Each antipodal distance regular graph is a covering graph of a smaller (usually primitive) distance regular graph; the antipodal distance graphs of diameter three are covers of the complete graph, and are the first non-trivial case. Many of the known examples are connected with geometric objects, such as projective planes and generalised quadrangles. We set up a classification scheme, and give new existence conditions and new constructions. A relationship with the theory of equi-isoclinic subspaces of Rm, as studied by Lemmens and Seidel, is investigated. © 1992.