%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.