On the sum of the Laplacian eigenvalues of a tree

0504847 - ÚI 2020 US eng J - Journal Article
Fritscher, E. - Hoppen, C. - Rocha, Israel - Trevisan, V.
On the sum of the Laplacian eigenvalues of a tree.
Linear Algebra and Its Applications. Roč. 435, č. 2 (2011), s. 371-399. ISSN 0024-3795. E-ISSN 1873-1856
Keywords : pi-electron energy * graph * Tree * Laplacian eigenvalues * Laplacian energy
Impact factor: 0.974, year: 2011

Given an n-vertex graph G = (V, E), the Laplacian spectrum of G is the set of eigenvalues of the Laplacian matrix L = D A, where D and A denote the diagonal matrix of vertex-degrees and the adjacency matrix of G, respectively. In this paper, we study the Laplacian spectrum of trees. More precisely, we find a new upper bound on the sum of the k largest Laplacian eigenvalues of every n-vertex tree, where k is an element of {1, ... , n}. This result is used to establish that the n-vertex star has the highest Laplacian energy over all n-vertex trees, which answers affirmatively to a question raised by Radenkovic and Gutman [10].
Permanent Link: http://hdl.handle.net/11104/0296396