Every nonsymmetric 4-class association scheme can be generated by a digraph

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-03-07 DOI:10.1016/j.disc.2025.114478

Yuefeng Yang

引用次数: 0

Abstract

A (di)graph Γ generates a commutative association scheme

X

if and only if the adjacency matrix of Γ generates the Bose-Mesner algebra of

X

. In [18, Theorem 1.1], Monzillo and Penjić proved that, except for amorphic symmetric association schemes, every 3-class association scheme can be generated by the adjacency matrix of a (di)graph. In this paper, we characterize when a commutative association scheme with exactly one pair of nonsymmetric relations can be generated by a digraph under certain assumptions. As an application, we show that each nonsymmetric 4-class association scheme can be generated by a digraph.

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.