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 distrib...

Full description

Saved in:
Bibliographic Details
Published inLinear algebra and its applications Vol. 598; pp. 165 - 185
Main Authors DeFord, Daryl, Rockmore, Daniel N.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.08.2020
American Elsevier Company, Inc
Subjects
Eigenvalues
Graph spectra
Graph theory
Linear algebra
Polynomials
Regular trees
Singular distributions
Trees
Graph spectra
Graph theory
05C50
Regular trees
Singular distributions
05C05
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2020.03.040