Edge-symmetric distance-regular coverings of complete graphs: the almost simple case
Let \(\Gamma\) be a distance-regular covering of a complete graph. It is well-known that \(\Gamma\) is an antipodal graph of diameter~\(3\) and the antipodal classes of \(\Gamma\) are the blocks of the covering. Moreover, the intersection array of \(\Gamma\) can be written as \((k, (r-1)\mu, 1; 1, \mu, k)\), where \(r\) is the order of the antipodal class. The authors have been working on the classification of \(\Gamma\) when \(\Gamma\) is edge-transitive. In the preceding papers, they have finished it in the case of \(r\in\{2, k, (k-1)/\mu\}\). In this paper, they tackle the case \(r\notin\{2, k, (k-1)/\mu\}\) and give the classification under the assumption that the action of \(\operatorname{Aut}(G)\) on the set of the untipodal classes is almost simple.
scientific article; zbMATH DE number 6979345
scientific article