Email this article Asymptotics and Arithmetical Properties of Complexity for Circulant Graphs
- Authors: Mednykh A.D.1,2, Mednykh I.A.1,2
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Affiliations:
- Sobolev Institute of Mathematics, Siberian Branch
- Novosibirsk State University
- Issue: Vol 97, No 2 (2018)
- Pages: 147-151
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225479
- DOI: https://doi.org/10.1134/S1064562418020138
- ID: 225479
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Abstract
Abstract—We study analytical and arithmetical properties of the complexity function for infinite families of circulant Cn(s1, s2,…, sk) C2n(s1, s2,…, sk, 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.
About the authors
A. D. Mednykh
Sobolev Institute of Mathematics, Siberian Branch; Novosibirsk State University
Author for correspondence.
Email: smedn@mail.ru
Russian Federation, Novosibirsk, 630090; Novosibirsk, 630090
I. A. Mednykh
Sobolev Institute of Mathematics, Siberian Branch; Novosibirsk State University
Email: smedn@mail.ru
Russian Federation, Novosibirsk, 630090; Novosibirsk, 630090
