On commutative association schemes and associated (directed) graphs
Combinatorics
2023-12-04 v2
Abstract
Let denote the Bose--Mesner algebra of a commutative -class association scheme (not necessarily symmetric), and denote a (strongly) connected (directed) graph with adjacency matrix . Under the assumption that belongs to , we describe the combinatorial structure of . Moreover, we provide an algebraic-combinatorial characterization of when generates . Among else, we show that, if is a commutative -class association scheme that is not an amorphic symmetric scheme, then we can always find a (directed) graph such that the adjacency matrix of generates the Bose--Mesner algebra of .
Cite
@article{arxiv.2307.11680,
title = {On commutative association schemes and associated (directed) graphs},
author = {Giusy Monzillo and Safet Penjić},
journal= {arXiv preprint arXiv:2307.11680},
year = {2023}
}