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

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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.

Original languageEnglish
Pages (from-to)467-485
Number of pages19
JournalArs Mathematica Contemporanea
Volume15
Issue number2
DOIs
Publication statusPublished - 2018

Keywords

  • Chebyshev polynomial
  • I-graph
  • Jacobian group
  • Petersen graph
  • Spanning tree

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