%A LIU Li, YUAN Hui, HE Huan %T Signless Laplacian Spectral Radius and Some Properties of Graphs %0 Journal Article %D 2022 %J Journal of Chaohu University %R 10.12152/j.issn.1672-2868.2022.03.007 %P 52-55 %V 24 %N 3 %U {http://xb.chu.edu.cn/CN/abstract/article_593.shtml} %8 2022-05-25 %X For any given simple graph G, the question of how to judge whether it has some structural properties has been explored by graph theory scholars. Because the spectrum of a graph can well reflect the structural properties of a graph and is easy for calculation, in recent years, many scholars have used the spectrum theory to study the related properties of a graph. In this paper, we first find the stability of the corresponding structural properties of graphs, then construct the corresponding closures of graphs; finally, by using the method of reductio ad absurdum, according to the signless Laplacian spectral radius of its complement, graph G with larger minimum degrees is the sufficient condition for s-connected, s-edge-connected, s-path-coverable, s-Hamiltonian, s-edge-Hamiltonian, s-Hamilton-connected or α(G)≤s.