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
收藏
页码：887 / 897
页数：11
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