A combinatorial proof of Bass's determinant formula for the zeta function of regular graphs
Combinatorics
2017-06-07 v2 Discrete Mathematics
Abstract
We give an elementary combinatorial proof of Bass's determinant formula for the zeta function of a finite regular graph. This is done by expressing the number of non-backtracking cycles of a given length in terms of Chebychev polynomials in the eigenvalues of the adjacency operator of the graph.
Keywords
Cite
@article{arxiv.1706.00851,
title = {A combinatorial proof of Bass's determinant formula for the zeta function of regular graphs},
author = {Bharatram Rangarajan},
journal= {arXiv preprint arXiv:1706.00851},
year = {2017}
}
Comments
13 pages, 5 figures