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On the distribution of Laplacian eigenvalues of trees

2013; Elsevier BV; Volume: 313; Issue: 21 Linguagem: Inglês

10.1016/j.disc.2013.06.017

1872-681X

Rodrigo O. Braga, Virgı́nia M. Rodrigues, Vilmar Trevisan,

Limits and Structures in Graph Theory

For a tree T with n vertices, we apply an algorithm due to Jacobs and Trevisan (2011) to study how the number of small Laplacian eigenvalues behaves when the tree is transformed by a transformation defined by Mohar (2007). This allows us to obtain a new bound for the number of eigenvalues that are smaller than 2. We also report our progress towards a conjecture on the number of eigenvalues that are smaller than the average degree.