Improved Lower Bounds on the Extrema of Eigenvalues of Graphs

被引：1
作者：
Linz, William [1 ]
机构：
[1] Univ South Carolina, Columbia, SC 29208 USA
来源：
GRAPHS AND COMBINATORICS | 2023年 / 39卷 / 04期
基金：
美国国家科学基金会;
关键词：
Eigenvalues; Icosahedral graph; kth largest eigenvalue;
D O I：
10.1007/s00373-023-02678-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this note, we improve the lower bounds for the maximum size of the kth largest eigenvalue of the adjacency matrix of a graph for several values of k. In particular, we show that closed blowups of the icosahedral graph improve the lower bound for the maximum size of the fourth largest eigenvalue of a graph, answering a question of Nikiforov.
引用
收藏
页数：4
相关论文
共 50 条
[31]   Extrema of Low Eigenvalues of the Dirichlet-Neumann Laplacian on a Disk [J].
Legendre, Eveline .
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2010, 62 (04) :808-826
[32]   On the Eigenvalues of Some Signed Graphs [J].
Souri, M. ;
Heydari, F. ;
Maghasedi, M. .
IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE, 2021, 45 (02) :635-639
[33]   Eigenvalues of complete multipartite graphs [J].
Delorme, C. .
DISCRETE MATHEMATICS, 2012, 312 (17) :2532-2535
[34]   On the Eigenvalues of Some Signed Graphs [J].
M. Souri ;
F. Heydari ;
M. Maghasedi .
Iranian Journal of Science and Technology, Transactions A: Science, 2021, 45 :635-639
[35]   EIGENVALUES AND EXPANSION OF REGULAR GRAPHS [J].
KAHALE, N .
JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY, 1995, 42 (05) :1091-1106
[36]   Extreme eigenvalues of nonregular graphs [J].
Cioaba, Sebastian M. ;
Gregory, David A. ;
Nikiforov, Vladimir .
JOURNAL OF COMBINATORIAL THEORY SERIES B, 2007, 97 (03) :483-486
[37]   A conjecture on the eigenvalues of threshold graphs [J].
Tura, Fernando C. .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2021, 612 :345-356
[38]   Average distance in graphs and eigenvalues [J].
Sivasubramanian, Sivaramakrishnan .
DISCRETE MATHEMATICS, 2009, 309 (10) :3458-3462
[39]   A note on eigenvalues of Cayley graphs [J].
Arnadottir, Arnbjoerg Soffia ;
Godsil, Chris .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2025, 721 :240-249
[40]   Universal bounds for eigenvalues of the biharmonic operator [J].
Wang, Qiaoling ;
Xia, Changyu .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 364 (01) :1-17
12345