On the second smallest and the largest normalized Laplacian eigenvalues of a graph

2016/03/14 by Xiaoguo Tian, Tian, Xiaoguo, Ligong Wang +3
Chemistry · Computer Science · Mathematics · #05C50 #15A18 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Synthesis and Properties of Aromatic Compounds

paper · pdf · doi:10.48550/arxiv.1603.04301

openalex publication_date 2016/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a simple connected graph with order n. Let L(G) be the normalized Laplacian matrix of G. Let λ_k(G) be the k-th smallest normalized Laplacian eigenvalue of G. Denote 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.

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