Complete signed graphs with largest maximum or smallest minimum eigenvalue

被引：3

作者：

Ghorbani, Ebrahim ^{[1
,2
]}

Majidi, Arezoo ^{[1
]}

机构：

[1] KN Toosi Univ Technol, Dept Math, POB 16765-3381, Tehran 163151618, Iran

[2] Univ Hamburg, Dept Math, Bundesstr 55 Geomatikum, D-20146 Hamburg, Germany

来源：

DISCRETE MATHEMATICS | 2024年 / 347卷 / 04期

关键词：

Signed graph; Seidel matrix; Index; Minimum eigenvalue; NUMBER;

D O I：

10.1016/j.disc.2023.113860

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we deal with extremal eigenvalues of the adjacency matrices of complete signed graphs. The complete signed graphs with maximal index (i.e. the largest eigenvalue) with n vertices and m <= ln(2)/4j negative edges have been already determined. We address the remaining case by characterizing those with m > ln(2)/4j negative edges. We also identify the unique signed graph with maximal index among complete signed graphs whose negative edges induce a tree of diameter at least d for any given d. This extends a recent result by Li, Lin, and Meng [Discrete Math. 346 (2023), 113250] who established the same result for d = 2. Finally, we prove that the smallest minimum eigenvalue of complete signed graphs with n vertices whose negative edges induce a tree is -root (n)/(2) -1 -1 + O(n1). (c) 2023 Elsevier B.V. All rights reserved.

引用

页数：14

共 17 条

[1]

[Anonymous], 1978, Annals of Discrete Mathematics

[2]

Belardo F., 2018, Art Discrete Appl. Math., V1

[3] Lifts, discrepancy and nearly optimal spectral cap [J].