On 3-equivalenced weakly distance-regular digraphs

TL;DR

This paper classifies 3-equivalenced weakly distance-regular digraphs assuming commutativity, advancing understanding of their structure and properties within algebraic combinatorics.

Contribution

It provides a classification of 3-equivalenced weakly distance-regular digraphs under the assumption of commutativity, a novel result in the study of algebraic graph theory.

Findings

Classification of 3-equivalenced weakly distance-regular digraphs

Identification of structural properties under commutativity

Extension of algebraic combinatorics knowledge

Abstract

A weakly distance-regular digraph is 3-equivalenced if its attached association scheme is 3-equivalenced. In this paper, we classify the family of such digraphs under the assumption of the commutativity.