Abstract
The Laplacian Estrada index of a graph G is denned as LEE(G) =Σni=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.
| Original language | English |
|---|---|
| Pages (from-to) | 777-782 |
| Number of pages | 6 |
| Journal | Match |
| Volume | 63 |
| Issue number | 3 |
| Publication status | Published - 2010 |
ASJC Scopus subject areas
- General Chemistry
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics