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
收藏
页码：2730 / 2734
页数：5
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