Spectral radius and maximum degree of connected graphs
نویسنده
چکیده
Given a connected irregular graph G of order n, write μ for the largest eigenvalue of its adjacency matrix, ∆ for its maximum degree, andD for its diameter. We prove that ∆− μ > 1 (D + 2)n and this bound is tight up to a constant factor. This improves previous results of Stevanović and Zhang, and extends a result of Alon and Sudakov.
منابع مشابه
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/n). This improves two recent results by Stevanović and Zhang, respectively. © 2007 Elsevier Inc. All rights reserved.
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تاریخ انتشار 2008