N ov 2 01 7 The number of spanning trees in circulant graphs , its arithmetic properties and asymptotic
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چکیده
In this paper, we develop a new method to produce explicit formulas for the number τ(n) of spanning trees in the undirected circulant graphs Cn(s1, s2, . . . , sk) and C2n(s1, s2, . . . , sk, n). Also, we prove that in both cases the number of spanning trees can be represented in the form τ(n) = p n a(n), where a(n) is an integer sequence and p is a prescribed natural number depending only of parity of n. Finally, we find an asymptotic formula for τ(n) through the Mahler measure of the associated Laurent polynomial L(z) = 2k − k ∑ i=1 (zi + zi).
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تاریخ انتشار 2017