Distance-regular graphs with strongly regular subconstituents
The main result of the article is a theorem about distance-regular graphs of diameter \(d\geq 3\) with all subconstituents being strongly regular graphs. The author shows that these are precisely the Taylor graphs \((d=3\) and \(|\Gamma_3 (u) |=1)\) or graphs with \(a_1= 0\), \(a_i\leq 1\) for \(2\leq i\leq d\). The result nicely complements the classification of strongly regular graphs with strongly regular subconstituents obtained by Cameron, Goethals and Seidel. The proof presented consists of a series of lemmas examining the possible parameters combined with an inventive use of previously known results.
scientific article; zbMATH DE number 1038957