Quasi-thin weakly distance-regular digraphs,I

TL;DR

This paper investigates quasi-thin weakly distance-regular digraphs, establishing that their valency is bounded above by 6, thereby advancing understanding of their structural limitations.

Contribution

It proves that the valency of any commutative quasi-thin weakly distance-regular digraph cannot exceed 6, providing a key structural bound.

Findings

Valency of such digraphs is at most 6

Provides structural bounds for quasi-thin weakly distance-regular digraphs

Advances classification of these digraphs

Abstract

A weakly distance-regular digraph is quasi-thin if the maximum value of its intersection numbers is 2. In this paper, we show that the valency of any commutative quasi-thin weakly distance-regular digraph is at most 6.