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arXiv · 1706.00851

A combinatorial proof of Bass's determinant formula for the zeta function of regular graphs

Bharatram Rangarajan
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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.

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Bharatram Rangarajan. 2017-06-06. A combinatorial proof of Bass's determinant formula for the zeta function of regular graphs. https://arxiv.org/abs/1706.00851

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