Locally semicomplete weakly distance-regular digraphs

TL;DR

This paper characterizes all locally semicomplete weakly distance-regular digraphs with the commutativity assumption, advancing understanding of their structure in graph theory.

Contribution

It provides a complete characterization of locally semicomplete weakly distance-regular digraphs assuming commutativity, a novel classification in the field.

Findings

Complete classification of such digraphs

Identification of structural properties under commutativity

Extension of weakly distance-regular digraph theory

Abstract

A digraph is semicomplete if any two vertices are connected by at least one arc and is locally semicomplete if the out-neighbourhood (resp. in-neighbourhood) of any vertex induces a semicomplete digraph. In this paper, we characterize all locally semicomplete weakly distance-regular digraphs under the assumption of commutativity.