Weakly distance-regular digraphs of valency three, II

TL;DR

This paper classifies a specific class of weakly distance-regular directed graphs with valency three, girth greater than two, and one arc type, completing their full characterization.

Contribution

It provides a complete classification of commutative weakly distance-regular digraphs of valency 3 under specified conditions, building on previous theorems.

Findings

Complete classification of the specified digraphs.

Determination of their structural properties.

Extension of existing theorems to this class.

Abstract

In this paper, we classify commutative weakly distance-regular digraphs of valency 3 with girth more than 2 and one type of arcs. Combining [8, Theorem 1.2], [10, Theorem 1.3] and [11, Theorem 1], commutative weakly distanceregular digraphs of valency 3 are completely determined.