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On Jacobian group and complexity of the I-graph I(n, k, l) through Chebyshev polynomials. / Mednykh, Ilya A.

In: Ars Mathematica Contemporanea, Vol. 15, No. 2, 2018, p. 467-485.

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

Harvard

Mednykh, IA 2018, 'On Jacobian group and complexity of the I-graph I(n, k, l) through Chebyshev polynomials', Ars Mathematica Contemporanea, vol. 15, no. 2, pp. 467-485. https://doi.org/10.26493/1855-3974.1355.576

APA

Mednykh, I. A. (2018). On Jacobian group and complexity of the I-graph I(n, k, l) through Chebyshev polynomials. Ars Mathematica Contemporanea, 15(2), 467-485. https://doi.org/10.26493/1855-3974.1355.576

Vancouver

Mednykh IA. On Jacobian group and complexity of the I-graph I(n, k, l) through Chebyshev polynomials. Ars Mathematica Contemporanea. 2018;15(2):467-485. doi: 10.26493/1855-3974.1355.576

Author

Mednykh, Ilya A. / On Jacobian group and complexity of the I-graph I(n, k, l) through Chebyshev polynomials. In: Ars Mathematica Contemporanea. 2018 ; Vol. 15, No. 2. pp. 467-485.

BibTeX

@article{ecba5c1182a94e79bcebad96fa2a7fd0,
title = "On Jacobian group and complexity of the I-graph I(n, k, l) through Chebyshev polynomials",
abstract = "We consider a family of I-graphs I(n,k,l), which is a generalization of the class of generalized Petersen graphs. In the present paper, we provide a new method for counting Jacobian group of the I-graph I(n,k,l). We show that the minimum number of generators of Jac(I(n,k,l)) is at least two and at most 2k+2l−1. Also, we obtain a closed formula for the number of spanning trees of I(n,k,l) in terms of Chebyshev polynomials. We investigate some arithmetical properties of this number and its asymptotic behaviour.",
keywords = "Chebyshev polynomial, I-graph, Jacobian group, Petersen graph, Spanning tree",
author = "Mednykh, {Ilya A.}",
note = "Publisher Copyright: {\textcopyright} 2018 Society of Mathematicians, Physicists and Astronomers of Slovenia. All rights reserved.",
year = "2018",
doi = "10.26493/1855-3974.1355.576",
language = "English",
volume = "15",
pages = "467--485",
journal = "Ars Mathematica Contemporanea",
issn = "1855-3966",
publisher = "DMFA Slovenije",
number = "2",

}

RIS

TY - JOUR

T1 - On Jacobian group and complexity of the I-graph I(n, k, l) through Chebyshev polynomials

AU - Mednykh, Ilya A.

N1 - Publisher Copyright: © 2018 Society of Mathematicians, Physicists and Astronomers of Slovenia. All rights reserved.

PY - 2018

Y1 - 2018

N2 - We consider a family of I-graphs I(n,k,l), which is a generalization of the class of generalized Petersen graphs. In the present paper, we provide a new method for counting Jacobian group of the I-graph I(n,k,l). We show that the minimum number of generators of Jac(I(n,k,l)) is at least two and at most 2k+2l−1. Also, we obtain a closed formula for the number of spanning trees of I(n,k,l) in terms of Chebyshev polynomials. We investigate some arithmetical properties of this number and its asymptotic behaviour.

AB - We consider a family of I-graphs I(n,k,l), which is a generalization of the class of generalized Petersen graphs. In the present paper, we provide a new method for counting Jacobian group of the I-graph I(n,k,l). We show that the minimum number of generators of Jac(I(n,k,l)) is at least two and at most 2k+2l−1. Also, we obtain a closed formula for the number of spanning trees of I(n,k,l) in terms of Chebyshev polynomials. We investigate some arithmetical properties of this number and its asymptotic behaviour.

KW - Chebyshev polynomial

KW - I-graph

KW - Jacobian group

KW - Petersen graph

KW - Spanning tree

UR - http://www.scopus.com/inward/record.url?scp=85062831812&partnerID=8YFLogxK

U2 - 10.26493/1855-3974.1355.576

DO - 10.26493/1855-3974.1355.576

M3 - Article

AN - SCOPUS:85062831812

VL - 15

SP - 467

EP - 485

JO - Ars Mathematica Contemporanea

JF - Ars Mathematica Contemporanea

SN - 1855-3966

IS - 2

ER -

ID: 28012547