English

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

Combinatorics 2017-03-22 v1

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

Cite

@article{arxiv.1703.07058,
  title  = {On Jacobian group and complexity of I-graph I(n,k,l) through Chebyshev polynomials},
  author = {Ilya Mednykh},
  journal= {arXiv preprint arXiv:1703.07058},
  year   = {2017}
}

Comments

17. arXiv admin note: substantial text overlap with arXiv:1612.03372