A note on the Laplacian Estrada index of trees

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

  • Hanyuan Deng
  • Jie Zhang

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)777-782
Journal / PublicationMatch
Volume63
Issue number3
Publication statusPublished - 2010

Abstract

The Laplacian Estrada index of a graph G is denned as LEE(G) =Σn i=1 eμi, where μ1 ≥ μ2 ≥... ≥ μn-1 ≥ μn = 0 are the eigenvalues of its Laplacian matrix. An unsolved problem in [19] is whether Sn(3, n - 3) or Cn(n -5) has the third maximal Laplacian Estrada index among all trees on n vertices, where Sn(3, n - 3) is the double tree formed by adding an edge between the centers of the stars S3 and Sn-3 and Cn(n - 5) is the tree formed by attaching n - 5 pendent vertices to the center of a path P 5. In this paper, we partially answer this problem, and prove that LEE(Sn(3,n - 3)) > LEE{Cn(n - 5)) and Cn(n - 5) cannot have the third maximal Laplacian Estrada index among all trees on n vertices.

Citation Format(s)

A note on the Laplacian Estrada index of trees. / Deng, Hanyuan; Zhang, Jie.
In: Match, Vol. 63, No. 3, 2010, p. 777-782.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review