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Ars Combinatoria

  • Research article

Sharp Upper Bounds for the Largest Laplacian Eigenvalue of Mixed Graphs

Gui-Xian Tian1, Ting-Zhu Huang2, Shu-Yu Cui3
1College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua, Zhejiang, 321004, P.R. China
2School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611781, P.R. China
3Xingzhi College, Zhejiang Normal University, Jinhua, Zhejiang, 21004, P.R. China
  • Published: 31/10/2013

Abstract

The paper presents two sharp upper bounds for the largest Laplacian eigenvalue of mixed graphs in terms of the degrees and the average \(2\)-degrees, which improve and generalize the main results of Zhang and Li [Linear Algebra Appl.\(353(2002)11-20]\),Pan (Linear Algebra Appl.\(355(2002)287-295]\),respectively. Moreover, we also characterize some extreme graphs which attain these upper bounds. In last, some examples show that our bounds are improvement on some known bounds in some cases.

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Citation
Gui-Xian Tian, Ting-Zhu Huang, Shu-Yu Cui. Sharp Upper Bounds for the Largest Laplacian Eigenvalue of Mixed Graphs[J], Ars Combinatoria, Volume 112. 361-371. .