A combinatorial proof of Bass's determinant formula for the zeta function of regular graphs
arXiv:1706.00851
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.
13 pages, 5 figures