Remarks on Bounds of Normalized Laplacian Eigenvalues of Graphs

2015/06/18 by Milovanovic, Emina I., Milovanovic, Igor Z.
#05C50 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1506.05762

Abstract

Let G be a connected undirected graph with n, n≥ 3, vertices and m edges. Denote by ρ₁ ≥ ρ₂ ≥ ⋯ > ρ_n =0 the normalized Laplacian eigenvalues of G. Upper and lower bounds of ρ_i, i=1,2,… , n-1, are determined in terms of n and general Randi' c index, R_-1.

Related

• A few properties of the eigenvalues of normalized graph Laplacian
• On the second smallest and the largest normalized Laplacian eigenvalues of a graph
• Full characterization of graphs having certain normalized Laplacian eigenvalue of multiplicity n-3
• Upper bound for the Laplacian eigenvalues of a graph
• Normalized Laplacian eigenvalues of hypergraphs