Topologies and Laplacian spectra of a deterministic uniform recursive tree

Abstract

The uniform recursive tree (URT) is one of the most important models and has been successfully applied to many fields. Here we study exactly the topological characteristics and spectral properties of the Laplacian matrix of a deterministic uniform recursive tree, which is a deterministic version of URT. Firstly, from the perspective of complex networks, we determine the main structural characteristics of the deterministic tree. The obtained vigorous results show that the network has an exponential degree distribution, small average path length, power-law distribution of node betweenness, and positive degree-degree correlations. Then we determine the complete Laplacian spectra (eigenvalues) and their corresponding eigenvectors of the considered graph. Interestingly, all the Laplacian eigenvalues are distinct.

7 pages, 1 figures, definitive version accepted for publication in EPJB

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Cited by in corpus (4)

• Eigenvalues of normalized Laplacian matrices of fractal trees and dendrimers: Analytical results and applications
• Explicit determination of mean first-passage time for random walks on deterministic uniform recursive trees
• Structural and spectral properties of a family of deterministic recursive trees: Rigorous solutions
• Spectrum of the tight-binding model on Cayley Trees and comparison with Bethe Lattices