The graphs with all but two eigenvalues equal to ±1

被引：0

作者：

Cioaba, Sebastian M. ^{[1
]}

Haemers, Willem H. ^{[2
]}

Vermette, Jason R. ^{[1
]}

Wong, Wiseley ^{[3
]}

机构：

[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

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

[3] Univ Calif San Diego, Dept Math, San Diego, CA 92103 USA

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2015年 / 41卷 / 03期

关键词：

Graph; Adjacency matrix; Friendship graph; Spectral characterization;

D O I：

10.1007/s10801-014-0557-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We determine all graphs whose adjacency matrices have at most two eigenvalues (multiplicities included) different from +/- 1 and decide which of these graphs are determined by their spectrum. This includes the so-called friendship graphs, which consist of a number of edge-disjoint triangles meeting in one vertex. It turns out that the friendship graph is determined by its spectrum, except when the number of triangles equals sixteen.

引用

页码：887 / 897

页数：11

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