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 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 τ (n) = p n a(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 τ (n) through the Mahler measure of the associated Laurent polynomial L(z) = 2k − k i=1 (z s i + z −s i ).
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