On the local structure of distance-regular Mathon graphs

We study the structure of local subgraphs of distance-regular Mathon graphs of even valency. We describe some infinite series of locally $\Delta$-graphs of this family, where $\Delta$ 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.