Asymptotics and Arithmetical Properties of Complexity for Circulant Graphs

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Asymptotics and Arithmetical Properties of Complexity for Circulant Graphs. / Mednykh, A. D.; Mednykh, I. A.

In: Doklady Mathematics, Vol. 97, No. 2, 01.03.2018, p. 147-151.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{301c183ea9964dae9fbb82241ecb0ee4,

title = "Asymptotics and Arithmetical Properties of Complexity for Circulant Graphs",

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.",

keywords = "SPANNING TREE FORMULAS, CHEBYSHEV POLYNOMIALS, NUMBER",

author = "Mednykh, {A. D.} and Mednykh, {I. A.}",

note = "Publisher Copyright: {\textcopyright} 2018, Pleiades Publishing, Ltd.",

year = "2018",

month = mar,

day = "1",

doi = "10.1134/S1064562418020138",

language = "English",

volume = "97",

pages = "147--151",

journal = "Doklady Mathematics",

issn = "1064-5624",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - Asymptotics and Arithmetical Properties of Complexity for Circulant Graphs

AU - Mednykh, A. D.

AU - Mednykh, I. A.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - 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.

AB - 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.

KW - SPANNING TREE FORMULAS

KW - CHEBYSHEV POLYNOMIALS

KW - NUMBER

UR - http://www.scopus.com/inward/record.url?scp=85047239741&partnerID=8YFLogxK

U2 - 10.1134/S1064562418020138

DO - 10.1134/S1064562418020138

M3 - Article

AN - SCOPUS:85047239741

VL - 97

SP - 147

EP - 151

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 2

ER -

ID: 13487835