On a family of divisible design digraphs

Abstract

For every odd prime power q, a family of pairwise nonisomorphic normal arc-transitive divisible design Cayley digraphs with isomorphic neighborhood designs over a Heisenberg group of order q3 is constructed. It is proved that these digraphs are not distinguished by the Weisfeiler-Leman algorithm and have the Weisfeiler-Leman dimension 3.

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