Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topologies and Laplacian spectra of a deterministic uniform recursive
  tree   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.

29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org