文献类型：期刊文献

英文题名：Eigenvalues and toughness of regular graphs

作者：Chen, Yuanyuan[1];Lin, Huiqiu[1,2];Wang, Zhiwen[2]

机构：[1]Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830017, Xinjiang, Peoples R China;[2]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2025

卷号：348

期号：5

外文期刊名：DISCRETE MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001408748100001)】；

基金：This research is supported by Natural Science Foundation of Xinjiang Uygur Autonomous Region (No. 2023D01C165), National Natural Science Foundation of China (Nos. 12271162, 12301438, 12326372, 12326373 and 12401468), Natural Science Foundation of Shanghai (No. 22ZR1416300), the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning (No. TP2022031) and the Chenguang Program of Shanghai Education Development Foundation and Shanghai Municipal Education Commission (No. 23CGA37).

语种：英文

外文关键词：(Bipartite)toughness; Eigenvalue; Regular graph

摘要：The toughness of a graph G, denoted by t(G),is defined as t(G)=min {|S|/c(G-S):S subset of V(G)and c(G-S)>1}. The bipartite toughness tau(G)of a non-complete bipartite graph G= (X,Y)is defined as tau(G)=min {|S|/c(G-S):S subset of X or S subset of Y , and c(G-S)>1}. Incorporating the toughness and eigenvalues of a graph, we provide two sufficient eigenvalue conditions for a regular graph to be 1/b-tough for a positive integer b. which extend a significant result by Ciolba and Wong [10]. For a regular bipartite graph, it is proved that tau (G) >= 1. We further show a sufficient eigenvalue condition with the second largest eigenvalue for a regular bipar te graph having bipartite toughness more than 1.
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