Asymptotics and Arithmetical Properties of Complexity for Circulant Graphs |
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| Authors: | A. D. Mednykh I. A. Mednykh |
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| Affiliation: | 1.Sobolev Institute of Mathematics, Siberian Branch,Russian Academy of Sciences,Novosibirsk,Russia;2.Novosibirsk State University,Novosibirsk,Russia |
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| Abstract: | Abstract—We study analytical and arithmetical properties of the complexity function for infinite families of circulant C n (s1, s2,…, s k ) C2n(s1, s2,…, s k , n). Exact analytical formulas for the complexity functions of these families are derived, and their asymptotics are found. As a consequence, we show that the thermodynamic limit of these families of graphs coincides with the small Mahler measure of the accompanying Laurent polynomials. |
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