无符号拉普拉斯谱半径与图的若干性质

Signless Laplacian Spectral Radius and Some Properties of Graphs

对于给定的简单图G,如何判断图G具有某种结构性质,这一问题一直广受图论学者们的青睐。由于图的谱能够很好地反映图的结构性质且便于计算,近年来,诸多学者利用图谱理论来研究图的相关性质。首先找到了原图对应结构性质的稳定性,其次构造原图的对应闭包,最后利用反证法,根据补图的无符号拉普拉斯谱半径分别给出了具有较大最小度的图G是s-连通、s-边-连通、s-路-覆盖、s-哈密尔顿、s-边-哈密尔顿、s-哈密尔顿-连通或α(G)≤s的充分条件。

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, sHamilton-connected or α(G)≤s.