On the largest eigenvalue of non-regular graphs

We study the spectral radius of connected non-regular graphs. Let λ1(n,Δ) be the maximum spectral radius among all connected non-regular graphs with n vertices and maximum degree Δ. We prove that Δ − λ1(n,Δ) = Θ(Δ/n2). This improves two recent results by Stevanovi´c and Zhang, respectively. © 2007 Elsevier Inc. All rights reserved.

• Type: Journal
• Year: 2007
• Where: JCT
• Authors: Bolian Liu, Jian Shen, Xinmao Wang
• Keywords: JCT 2007, Maximum Spectral Radius, Non-regular Graphs, Spectral Radius