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arXiv · 1811.03801

On complexity of cyclic coverings of graphs

Y. S. Kwon·A. D. Mednykh·I. A. Mednykh
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Abstract

By complexity of a finite graph we mean the number of spanning trees in the graph. The aim of the present paper is to give a new approach for counting complexity $τ(n)$ of cyclic $n$-fold coverings of a graph. We give an explicit analytic formula for $τ(n)$ in terms of Chebyshev polynomials and find its asymptotic behavior as $n\to\infty$ through the Mahler measure of the associated voltage polynomial. We also prove that $F(x)=\sum\limits_{n=1}^\inftyτ(n)x^n$ is a rational function with integer coefficients.

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Y. S. Kwon, A. D. Mednykh, I. A. Mednykh. 2018-11-09. On complexity of cyclic coverings of graphs. https://arxiv.org/abs/1811.03801

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