On the Local Structure of Mathon Distance-Regular Graphs

Abstract

We study the structure of local subgraphs of distance-regular Mathon graphs of even valency. We describe some infinite series of locally Δ-graphs of this family, where Δ is a strongly regular graph that is the union of affine polar graphs of type “–,” a pseudogeometric graph for _pG_l(s, l), or a graph of rank 3 realizable by means of the van Lint–Schrijver scheme. We show that some Mathon graphs are characterizable by their intersection arrays in the class of vertex-transitive graphs.