文献类型：期刊文献

英文题名：Toughness, hamiltonicity and spectral radius in graphs

作者：Fan, Dandan[1,2];Lin, Huiqiu[1];Lu, Hongliang[3]

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China;[2]Xinjiang Agr Univ, Coll Math & Phys, Urumqi 830052, Xinjiang, Peoples R China;[3]Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China

年份：2023

卷号：110

外文期刊名：EUROPEAN JOURNAL OF COMBINATORICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000949894400001)】；

基金：? This work are supported by the National Natural Science Foundation of China (Grant Nos. 12271162 and 12271425) , Natural Science Foundation of Shanghai, China (No. 22ZR1416300) and sponsored by Natural Science Foundation of Xinjiang Uygur Autonomous Region (Grant Nos. 2022D01B103) .

语种：英文

外文关键词：Toughness; Hamiltonian cycle; Spectral radius

摘要：The study of the existence of Hamiltonian cycles in a graph is a classical problem in graph theory. By incorporating toughness and spectral conditions, we can consider Chvatal's conjecture from another perspective: What is the spectral condition to guarantee the existence of a Hamiltonian cycle among t-tough graphs? We first give the answer to 1-tough graphs, i.e. if rho(G) > rho(Mn), then G contains a Hamiltonian cycle, unless G similar to= Mn, where Mn = K1 backward difference K+3 n-4 and K+3n-4 is the graph obtained from 3K1 boolean OR Kn-4 by adding three independent edges between 3K1 and Kn-4. The Brouwer's toughness theorem states that every dregular connected graph always has t(G) > lambda d - 1 where lambda is the second largest absolute eigenvalue of the adjacency matrix. In this paper, we extend the result in terms of its spectral radius, i.e. we provide a spectral condition for a graph to be 1-tough with minimum degree delta and to be t-tough, respectively.(c) 2023 Elsevier Ltd. All rights reserved.