On Jacobian group and complexity of the generalized Petersen graph GP(n,k) through Chebyshev polynomials

Y. S. Kwon; A. D. Mednykh; I. A. Mednykh

doi:10.1016/j.laa.2017.04.032

On Jacobian group and complexity of the generalized Petersen graph GP(n,k) through Chebyshev polynomials

Y. S. Kwon, A. D. Mednykh, I. A. Mednykh

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

7 Цитирования (Scopus)

Аннотация

In the present paper we give a new method for calculating Jacobian group Jac(GP(n,k)) of the generalized Petersen graph GP(n,k). We show that the minimum number of generators of Jac(GP(n,k)) is at least two and at most 2k+1. Both estimates are sharp. Also, we obtain a closed formula for the number of spanning trees of GP(n,k) in terms of Chebyshev polynomials and investigate some arithmetical properties of this number.

Язык оригинала	английский
Страницы (с-по)	355-373
Число страниц	19
Журнал	Linear Algebra and Its Applications
Том	529
DOI	https://doi.org/10.1016/j.laa.2017.04.032
Состояние	Опубликовано - 15 сен 2017

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10.1016/j.laa.2017.04.032

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abstract = "In the present paper we give a new method for calculating Jacobian group Jac(GP(n,k)) of the generalized Petersen graph GP(n,k). We show that the minimum number of generators of Jac(GP(n,k)) is at least two and at most 2k+1. Both estimates are sharp. Also, we obtain a closed formula for the number of spanning trees of GP(n,k) in terms of Chebyshev polynomials and investigate some arithmetical properties of this number.",

keywords = "Chebyshev polynomial, Jacobian group, Laplacian matrix, Petersen graph, Spanning tree, SANDPILE GROUP, NUMBER, SPANNING TREE FORMULAS, CIRCULANT",

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On Jacobian group and complexity of the generalized Petersen graph GP(n,k) through Chebyshev polynomials. / Kwon, Y. S.; Mednykh, A. D.; Mednykh, I. A.

В: Linear Algebra and Its Applications, Том 529, 15.09.2017, стр. 355-373.

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

TY - JOUR

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AU - Kwon, Y. S.

AU - Mednykh, A. D.

AU - Mednykh, I. A.

PY - 2017/9/15

Y1 - 2017/9/15

N2 - In the present paper we give a new method for calculating Jacobian group Jac(GP(n,k)) of the generalized Petersen graph GP(n,k). We show that the minimum number of generators of Jac(GP(n,k)) is at least two and at most 2k+1. Both estimates are sharp. Also, we obtain a closed formula for the number of spanning trees of GP(n,k) in terms of Chebyshev polynomials and investigate some arithmetical properties of this number.

AB - In the present paper we give a new method for calculating Jacobian group Jac(GP(n,k)) of the generalized Petersen graph GP(n,k). We show that the minimum number of generators of Jac(GP(n,k)) is at least two and at most 2k+1. Both estimates are sharp. Also, we obtain a closed formula for the number of spanning trees of GP(n,k) in terms of Chebyshev polynomials and investigate some arithmetical properties of this number.

KW - Chebyshev polynomial

KW - Jacobian group

KW - Laplacian matrix

KW - Petersen graph

KW - Spanning tree

KW - SANDPILE GROUP

KW - NUMBER

KW - SPANNING TREE FORMULAS

KW - CIRCULANT

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DO - 10.1016/j.laa.2017.04.032

M3 - Article

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VL - 529

SP - 355

EP - 373

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

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