On the largest eigenvalue of non-regular graphs
نویسندگان
چکیده
منابع مشابه
A 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.
متن کاملOn 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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∗Received by the editors November 21, 2007. Accepted for publication February 15, 2008. Handling Editor: Stephen J. Kirkland. †School of Mathematics Sciences, South China Normal University, Guangzhou, 510631, P.R. China ([email protected], [email protected]). This work was supported by the National Natural Science Foundation of China (No.10771080) and by DF of the Ministry of Education of China...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2007
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2007.02.008