Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Spectrum of Finite, Rooted Homogeneous Trees   In this paper we study the adjacency spectrum of families of finite rooted
trees with regular branching properties. In particular, we show that in the
case of constant branching, the eigenvalues are realized as the roots of a
family of generalized Fibonacci polynomials and produce a limiting distribution
for the eigenvalues as the tree depth goes to infinity. We indicate how these
results can be extended to periodic branching patterns and also provide a
generalization to higher order simplicial complexes.

30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org