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

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

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	355-373
Number of pages	19
Journal	Linear Algebra and Its Applications
Volume	529
DOIs	https://doi.org/10.1016/j.laa.2017.04.032
Publication status	Published - 15 Sep 2017

Keywords

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

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10.1016/j.laa.2017.04.032

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

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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note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

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T1 - On Jacobian group and complexity of the generalized Petersen graph GP(n,k) through Chebyshev polynomials

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

UR - http://www.scopus.com/inward/record.url?scp=85019123036&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2017.04.032

DO - 10.1016/j.laa.2017.04.032

M3 - Article

AN - SCOPUS:85019123036

VL - 529

SP - 355

EP - 373

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -

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

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Keywords

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