On combinatorial structure and algebraic characterizations of distance-regular digraphs
Combinatorics
2024-04-08 v1
Abstract
Let denote a simple strongly connected digraph with vertex set , diameter , and let denote the set of distance- matrices of . Let denote a partition of , where . The digraph is distance-regular if and only if is a commutative association scheme. In this paper, we describe the combinatorial structure of in the sense of equitable partition, and from it we derive several new algebraic characterizations of such a graph, including the spectral excess theorem for distance-regular digraph. Along the way, we also rediscover all well-known algebraic characterizations of such graphs.
Cite
@article{arxiv.2404.03910,
title = {On combinatorial structure and algebraic characterizations of distance-regular digraphs},
author = {Giusy Monzillo and Safet Penić},
journal= {arXiv preprint arXiv:2404.03910},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:2403.00652