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Asymptotics and Arithmetical Properties of Complexity for Circulant Graphs

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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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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

    A. D. Mednykh & I. A. Mednykh

  2. Novosibirsk State University, Novosibirsk, 630090, Russia

    A. D. Mednykh & I. A. Mednykh

Authors
  1. A. D. Mednykh
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  2. I. A. Mednykh
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Correspondence to A. D. Mednykh.

Additional information

Original Russian Text © A.D. Mednykh, I.A. Mednykh, 2018, published in Doklady Akademii Nauk, 2018, Vol. 479, No. 4, pp. 363–367.

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Mednykh, A.D., Mednykh, I.A. Asymptotics and Arithmetical Properties of Complexity for Circulant Graphs. Dokl. Math. 97, 147–151 (2018). https://doi.org/10.1134/S1064562418020138

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  • DOI: https://doi.org/10.1134/S1064562418020138

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