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