Journal of Chaohu University ›› 2022, Vol. 24 ›› Issue (3): 52-55.doi: 10.12152/j.issn.1672-2868.2022.03.007

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Signless Laplacian Spectral Radius and Some Properties of Graphs

LIU Li,YUAN Hui,HE Huan:School of Mathematics and Physics, Anqing Normal University   

  1. School of Mathematics and Physics, Anqing Normal University, Anqing Anhui 246133
  • Received:2021-11-25 Online:2022-05-25 Published:2022-09-06

Abstract: 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.

Key words: signless Laplacian spectral radius, stability, closure, minimum degree

CLC Number: 

  • O157.5