Dual concepts of almost distance-regularity and the spectral excess theorem

被引：6

作者：

Dalfo, C. ^{[1
]}

van Dam, E. R. ^{[2
]}

Fiol, M. A. ^{[1
]}

Garriga, E. ^{[1
]}

机构：

[1] Univ Politecn Cataluna, Dept Matemat Aplicada 4, Barcelona, Catalonia, Spain

[2] Tilburg Univ, Dept Econometr & OR, NL-5000 LE Tilburg, Netherlands

来源：

DISCRETE MATHEMATICS | 2012年 / 312卷 / 17期

关键词：

Distance-regular graph; Distance matrices; Eigenvalues; Idempotents; Local spectrum; Predistance polynomials;

D O I：

10.1016/j.disc.2012.03.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Generally speaking, 'almost distance-regular' graphs share some, but not necessarily all, of the regularity properties that characterize distance-regular graphs. In this paper we propose two new dual concepts of almost distance-regularity, thus giving a better understanding of the properties of distance-regular graphs. More precisely, we characterize m-partially distance-regular graphs and j-punctually eigenspace distance-regular graphs by using their spectra. Our results can also be seen as a generalization of the so-called spectral excess theorem for distance-regular graphs, and they lead to a dual version of it. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：2730 / 2734

页数：5

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