On Jacobian group and complexity of the generalized Petersen graph GP(n,k) through Chebyshev polynomials
Y. S. Kwon (1), A. D. Mednykh (2,3,4), I. A. Mednykh (2,3,4) ((1), Yengnam University, Yengnam, South Korea, (2) Sobolev Institute of, Mathematics, Novosibirsk, Russia, (3) Novosibirsk State University,, Novosibirsk, Russia, (4) Siberian Federal University, Krasnoyarsk, Russia)
TL;DR
This paper introduces an efficient algorithm for computing the Jacobian group of generalized Petersen graphs and derives a closed-form formula for their spanning trees using Chebyshev polynomials.
Contribution
It presents a novel simple algorithm for Jacobian group enumeration and a closed formula for spanning trees in GP(n,k) graphs based on Chebyshev polynomials.
Findings
Efficient algorithm for Jacobian group counting
Closed-form formula for spanning trees
Use of Chebyshev polynomials in graph analysis
Abstract
In the present paper we find a simple algorithm for counting Jacobian group of the generalized Petersen graph GP(n,k). Also, we obtain a closed formula for the number of spanning trees of this graph in terms of Chebyshev polynomials.
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Taxonomy
TopicsGraph theory and applications · Advanced Combinatorial Mathematics · Topological and Geometric Data Analysis