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

2017/03/21 by Mednykh, Ilya · 1 citation
#05C30 #39A10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.07058

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.

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• The number of rooted spanning forests of bicirculant graphs

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