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Ars Combinatoria

  • Research article

The Minimal Limit Point of the Third Largest Laplacian Eigenvalues of Graphs

Yarong Wu1,2, Jinlong Shu1,3, Yuan Hong1
1Department of Mathematics, East China Normal University, shanghai, 200241, China
2Department of Mathematics, Shanghai Maritime University, Shanghai, 200135, China
3Key Laboratory of Geographic Information Science Ministry of Education, East China Normal University, Shanghai, 200241, China
  • Published: 31/01/2012

Abstract

Let \(G\) be a simple connected graph with \(n\) vertices. Denoted by \(L(G)\) the Laplacian matrix of G. In this paper, we present a sequence of graphs \({G_n}\) with \(\lim\limits_{n\to \infty} \mu_3(G_n) = 1.5550\) by investigating the eigenvalues of the line graphs of \({G_n}\). Moreover, we prove that the limit is the minimal limit point of the third largest Laplacian eigenvalues of graphs.

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Citation
Yarong Wu, Jinlong Shu, Yuan Hong. The Minimal Limit Point of the Third Largest Laplacian Eigenvalues of Graphs[J], Ars Combinatoria, Volume 103. 119-127. .