Weakly distance-regular digraphs whose underlying graphs are distance-regular,II

TL;DR

This paper classifies all commutative weakly distance-regular digraphs with underlying graphs being Johnson or folded Johnson graphs, extending previous classifications to new graph families.

Contribution

It provides a complete classification of such digraphs when the underlying graphs are Johnson or folded Johnson graphs, expanding the understanding of their structure.

Findings

Classified all commutative weakly distance-regular digraphs with Johnson underlying graphs.

Extended previous classifications beyond Hamming, folded n-cubes, and Doob graphs.

Contributed to the theory of weakly distance-regular digraphs and their underlying graphs.

Abstract

Weakly distance-regular digraphs are a natural directed version of distance-regular graphs. In [16], we classified all commutative weakly distance-regular digraphs whose underlying graphs are Hamming graphs, folded n-cubes, or Doob graphs. In this paper, we classify all commutative weakly distance-regular digraphs whose underlying graphs are Johnson graphs or folded Johnson graphs.