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

Ilya A. Mednykh

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


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

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DOI: https://doi.org/10.26493/1855-3974.1355.576

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications