m-Distance-regular graphs and their relation to multivariate P-polynomial association schemes

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2024-07-24 DOI:10.1016/j.disc.2024.114179

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引用次数: 0

Abstract

An association scheme is P-polynomial if and only if it consists of the distance matrices of a distance-regular graph. Recently, bivariate P-polynomial association schemes of type $(α, β)$ were introduced by Bernard et al., and multivariate P-polynomial association schemes were later defined by Bannai et al. In this paper, the notion of m-distance-regular graph is defined and shown to give a graph interpretation of the multivariate P-polynomial association schemes. Various examples are provided. Refined structures and additional constraints for multivariate P-polynomial association schemes and m-distance-regular graphs are also considered. In particular, bivariate P-polynomial schemes of type $(α, β)$ are discussed, and their connection to 2-distance-regular graphs is established.

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米距离不规则图及其与多变量 P 多项式关联方案的关系

当且仅当关联方案由距离规则图的距离矩阵组成时，它才是 P 多项式关联方案。最近，Bernard 等人提出了 (α,β)类型的双变量 P 多项式关联方案，Bannai 等人随后定义了多变量 P 多项式关联方案。本文定义了 m 距离规则图的概念，并展示了多变量 P 多项式关联方案的图解释。文中提供了各种实例。本文还考虑了多变量 P 多项式关联方案和 m 距离不规则图的细化结构和附加约束。特别是讨论了 (α,β) 类型的双变量 P 多项式方案，并建立了它们与 2-距离不规则图的联系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.