Weakly distance-regular digraphs whose attached association schemes are regular

TL;DR

This paper investigates a specific class of weakly distance-regular directed graphs with regular association schemes, providing a characterization of mixed arcs and classifying such graphs with diameter 2.

Contribution

It offers a new characterization of mixed arcs and classifies weakly distance-regular digraphs with regular attached association schemes of diameter 2.

Findings

Characterization of mixed arcs in the studied digraphs

Classification of diameter 2 cases

Insights into the structure of regular association schemes

Abstract

In this paper, we study commutative weakly distance-regular digraphs whose attached association schemes are regular, and give a characterization of mixed arcs. As an application, we classify such digraphs of diameter 2.