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

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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.

Original languageEnglish
Pages (from-to)355-373
Number of pages19
JournalLinear Algebra and Its Applications
Volume529
DOIs
Publication statusPublished - 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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