A note on the Laplacian Estrada index of trees

Journal article

The Laplacian Estrada index of a graph G is defined as LEE(G) = Σⁿ_i=1 e^μ_i , where μ₁ ≥ μ₂ ≥ ··· ≥ 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 S₃ 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 P₅. 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.

Authors: Deng, H; Zhang, J

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Faculty of Science, University of Kragujevac
• Journal: MATCH Communications in Mathematical and in Computer Chemistry
• Volume: 63
• Issue: 3
• Pages: 777-782
• Publication date: 2010-01-01
• ISSN: 0340-6253
• Language: English