On the eigenvalues of signed complete graphs

被引：14

作者：

Akbari, S. ^{[1
]}

Dalvandi, S. ^{[2
]}

Heydari, F. ^{[2
]}

Maghasedi, M. ^{[2
]}

机构：

[1] Sharif Univ Technol, Dept Math Sci, Tehran, Iran

[2] Islamic Azad Univ, Karaj Branch, Dept Math, Karaj, Iran

来源：

LINEAR & MULTILINEAR ALGEBRA | 2019年 / 67卷 / 03期

基金：

美国国家科学基金会;

关键词：

Signed graph; adjacency matrix; complete graph;

D O I：

10.1080/03081087.2017.1403548

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let Gamma = (G, sigma) be a signed graph, where G is the underlying simple graph and sigma : E(G) -> {-, +} is the sign function on the edges of G. The adjacency matrix of a signed graph has - 1 or + 1 for adjacent vertices, depending on the sign of the connecting edges. In this paper, the eigenvalues of signed complete graphs are investigated. We prove that -1 and 1 are the eigenvalues of the signed complete graph with the multiplicity at least t if there are t + 1 vertices whose all incident edges are positive or negative, respectively. We study the spectrum of a signed complete graph whose negative edges induce an r-regular subgraph H. We obtain a relation between the eigenvalues of this signed complete graph and the eigenvalues of H.

引用

页码：433 / 441

页数：9