首页|On the smallest signless Laplacian eigenvalue of graphs
On the smallest signless Laplacian eigenvalue of graphs
扫码查看
点击上方二维码区域，可以放大扫码查看
原文链接
NSTL
Elsevier
For a simple graph G the signless Laplacian matrix of G is defined as D(G) + A(G), where A(G) and D(G) are the adjacency matrix and the diagonal matrix of vertex degrees of G, respectively. By the smallest signless Laplacian eigenvalue of G, denoted by q'(G), we mean the smallest eigenvalue of the signless Laplacian matrix of G. In this paper we study the smallest signless Laplacian eigenvalue of graphs and find some relations between this and the chromatic number of graphs. We prove that if G is a graph of order n and with chromatic number chi(G), then q'(G) <= q'(T(n, chi(G))), where T(n, t) is the Turan graph on n vertices and t parts. Using this inequality we obtain some bounds for q'(G) that improve the known previous bounds. (c) 2021 Elsevier Inc. All rights reserved.
NSTL
Elsevier
