Tutte Polynomials of Tensor Products of Signed Graphs and their Applications in Knot Theory

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dc.creatorDiao, Y.
dc.creatorHetyei, G.
dc.creatorHinson, K.
dc.date2007-02-12
dc.date.accessioned2026-07-07T07:46:20Z
dc.date.available2026-07-07T07:46:20Z
dc.descriptionIt is well-known that the Jones polynomial of an alternating knot is closely related to the Tutte polynomial of a special graph obtained from a regular projection of the knot. Relying on the results of Bollobás and Riordan, we introduce a generalization of Kauffman's Tutte polynomial of signed graphs for which describing the effect of taking a signed tensor product of signed graphs is very simple. We show that this Tutte polynomial of a signed tensor product of signed graphs may be expressed in terms of the Tutte polynomials of the original signed graphs by using a simple substitution rule. Our result enables us to compute the Jones polynomials of some large non-alternating knots. The combinatorics used to prove our main result is similar to Tutte's original way of counting ``activities'' and specializes to a new, perhaps simpler proof of the known formulas for the ordinary Tutte polynomial of the tensor product of unsigned graphs or matroids.
dc.description23 pages, 15 figures
dc.identifierhttps://arxiv.org/abs/math/0702328
dc.identifierhttp://arxiv.org/abs/math/0702328
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123797
dc.subjectGeometric Topology
dc.subjectCombinatorics
dc.subject57M25
dc.titleTutte Polynomials of Tensor Products of Signed Graphs and their Applications in Knot Theory
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