The number of spanning trees in circulant graphs, its arithmetic properties and asymptotic

In this paper, we develop a new method to produce explicit formulas for the number tau(n) of spanning trees in the undirected circulant graphs C-n(s(1), s(2), ... , s(k)) and C-2n(s(1), s(2), ... , s(k), n). Also, we prove that in both cases the number of spanning trees can be represented in the form tau(n) = pna(n)(2), where a(n) is an integer sequence and p is a prescribed natural number depending on the parity of n. Finally, we find an asymptotic formula for tau(n) through the Mahler measure of the associated Laurent polynomial L(z) = 2k - Sigma(k)(j=1)(z(sj) + z(-sj)). (C) 2019 Elsevier B.V. All rights reserved.