Geodesic
On Jacobian group and complexity of the I-graph I(n,k,l) through Chebyshev polynomials
Ars Mathematica Contemporanea, Tome 15 (2018) no. 2, pp. 467-485.

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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.
DOI : 10.26493/1855-3974.1355.576
Keywords: Spanning tree, Jacobian group, I-graph, Petersen graph, Chebyshev polynomial 
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Ilya A. Mednykh. On Jacobian group and complexity of the I-graph I(n,k,l) through Chebyshev polynomials. Ars Mathematica Contemporanea, Tome 15 (2018) no. 2, pp. 467-485. doi : 10.26493/1855-3974.1355.576. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1355.576/

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