Abstract
Let G be a simple connected graph with order n. Let L(G) and Q(G) be the normalized Laplacian and normalized signless Laplacian matrices of G, respectively. Let λk(G) be the k-th smallest normalized Laplacian eigenvalue of G. Denote by ρ(A) the spectral radius of the matrix A. In this paper, we study the behaviors of λ2(G) and ρ(L(G) ) when the graph is perturbed by three operations. We also study the properties of ρ(L(G) ) and X for the connected bipartite graphs, where X is a unit eigenvector of L(G) corresponding to ρ(L(G) ). Meanwhile we characterize all the simple connected graphs with ρ(L(G))=ρ(Q(G)).
Original language | English |
---|---|
Pages (from-to) | 628-644 |
Number of pages | 17 |
Journal | Acta Mathematicae Applicatae Sinica |
Volume | 37 |
Issue number | 3 |
DOIs | |
State | Published - Jul 2021 |
Keywords
- 05C50
- 15A18
- normalized Laplacian spectral radius
- normalized signless Laplacian spectral radius
- second smallest normalized Laplacian eigenvalue