Spectra of three-peg Hanoi towers graphs
Combinatorics
2021-07-07 v1
Abstract
We consider the relationship between the Laplacians on two sequences of planar graphs, one from the theory of self-similar groups and one from analysis on fractals. By establishing a spectral decimation map between these sequences we give an elementary calculation of the spectrum of the former, which was first computed by Grigorchuk and \v{S}uni\'{c}. Our method also gives a full description of the eigenfunctions.
Keywords
Cite
@article{arxiv.2107.02697,
title = {Spectra of three-peg Hanoi towers graphs},
author = {Brett Hungar and Gamal Mograby and Madison Phelps and Luke G. Rogers and Jonathan Wheeler},
journal= {arXiv preprint arXiv:2107.02697},
year = {2021}
}
Comments
22 pages, 9 figures