On the largest eigenvalue of non-regular graphs

Authors:
Bolian Liu;Jian Shen;Xinmao Wang
Affiliations:
Department of Mathematics, South China Normal University, Guangzhou 510631, PR China;Department of Mathematics, Texas State University, San Marcos, TX 78666, USA;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Venue:
Journal of Combinatorial Theory Series B
Year:
2007

Citing 2
Cited 0

A Remark on Minc's Maximal Eigenvector Bound for Positive Matrices

SIAM Journal on Matrix Analysis and Applications
The largest eigenvalue of nonregular graphs

Journal of Combinatorial Theory Series B

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Abstract

We study the spectral radius of connected non-regular graphs. Let @l"1(n,@D) be the maximum spectral radius among all connected non-regular graphs with n vertices and maximum degree @D. We prove that @D-@l"1(n,@D)=@Q(@D/n^2). This improves two recent results by Stevanovic and Zhang, respectively.