文献类型：期刊文献

英文题名：On the Eigenvalues of k-Degenerate Graphs

作者：Zhao, Yanhua[1];Park, Jongyook[2];Wang, Zhiwen[3]

机构：[1]Jiangsu Univ, Dept Math, Zhenjiang 212013, Jiangsu, Peoples R China;[2]Kyungpook Natl Univ, Dept Math, Daegu 41566, South Korea;[3]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2025

卷号：32

期号：2

起止页码：321

外文期刊名：ALGEBRA COLLOQUIUM

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001486819200005)】；

基金：& lowast;The first author was partly supported by NSFC (Nos. 11771141 and 12011530064) and the China Scholarship Council (CSC) (No. 202106740049). The second author was partly supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. NRF-2020R1A2C1A01101838). The third author was supported by NSFC (No. 12161141006) and CPSF (No. 2021M691671).

语种：英文

外文关键词：spectral radius; least eigenvalue; k-degenerate graphs

摘要：A graph G is k-degenerate if every subgraph of G has a vertex of degree at most k. The well-known Brualdi-Solheid problem asks for the maximum spectral radius of a graph belonging to a specified class of graphs and the characterization of extremal graphs. In this paper, we first characterize k-degenerate graphs with the minimum least eigenvalue. As an application, we give an answer to the Brualdi-Solheid problem for k-degenerate bipartite graphs. In addition, we give a new proof to determine the maximum signless Laplacian spectral radius and characterize the corresponding extremal graphs among k-degenerate graphs. We also raise a problem related to the second largest eigenvalues of k-degenerate graphs and solve this problem for 1-degenerate graphs.