منابع مشابه
The largest eigenvalue of nonregular graphs
We give an upper bound for the largest eigenvalue of a nonregular graph with n vertices and the largest vertex degree ∆.
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We prove that for all values of the edge probability p(n) the largest eigenvalue of a random graph G(n, p) satisfies almost surely: λ1(G) = (1 + o(1))max{ √ ∆, np}, where ∆ is a maximal degree of G, and the o(1) term tends to zero as max{ √ ∆, np} tends to infinity.
متن کاملA note on the largest eigenvalue of non-regular graphs
The spectral radius of connected non-regular graphs is considered. Let λ1 be the largest eigenvalue of the adjacency matrix of a graph G on n vertices with maximum degree ∆. By studying the λ1-extremal graphs, it is proved that if G is non-regular and connected, then ∆− λ1 > ∆+ 1 n(3n+∆− 8) . This improves the recent results by B.L. Liu et al. AMS subject classifications. 05C50, 15A48.
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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.
متن کاملGraphs with small second largest Laplacian eigenvalue
Let L(G) be the Laplacian matrix of G. In this paper, we characterize all of the connected graphs with second largest Laplacian eigenvalue no more than l; where l . = 3.2470 is the largest root of the equation μ3 − 5μ2 + 6μ − 1 = 0. Moreover, this result is used to characterize all connected graphs with second largest Laplacian eigenvalue no more than three. © 2013 Elsevier Ltd. All rights rese...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2016
ISSN: 0024-3795
DOI: 10.1016/j.laa.2016.03.037