Digraphs with few distinct eigenvalues

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-11-06 DOI:10.1016/j.laa.2024.10.028

M. Cavers , B. Miraftab

引用次数: 0

Abstract

This paper provides insight into the problem of characterizing digraphs (with loops permitted) that have few distinct adjacency eigenvalues, or equivalently, characterizing square

(0, 1)

-matrices that have few distinct eigenvalues. A spectral characterization of strongly connected digraphs whose adjacency matrix has exactly two distinct eigenvalues is given and constructions of such digraphs are described. In addition, bipartite digraphs with exactly three distinct eigenvalues are discussed.

查看原文本刊更多论文

特征值很少的数图

本文深入探讨了如何表征具有极少数不同邻接特征值的数图（允许有循环），或者等同于表征具有极少数不同特征值的方(0,1)矩阵。本文给出了邻接矩阵恰好有两个不同特征值的强连接数图的谱特征，并描述了此类数图的构造。此外，还讨论了具有恰好三个不同特征值的双方位图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.