## Abstract

The Laplacian Estrada index of a graph G is denned as LEE(G) =Σ^{n}_{i=1} e^{μi}, where μ_{1} ≥ μ_{2} ≥... ≥ μ_{n-1} ≥ μ_{n} = 0 are the eigenvalues of its Laplacian matrix. An unsolved problem in [19] is whether S_{n}(3, n - 3) or C_{n}(n -5) has the third maximal Laplacian Estrada index among all trees on n vertices, where S_{n}(3, n - 3) is the double tree formed by adding an edge between the centers of the stars S_{3} and S_{n-3} and C_{n}(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(S_{n}(3,n - 3)) > LEE{C_{n}(n - 5)) and C_{n}(n - 5) cannot have the third maximal Laplacian Estrada index among all trees on n vertices.

Original language | English |
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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