Partial duality and Bollobás and Riordan’s ribbon graph polynomial |
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Authors: | Iain Moffatt |
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Institution: | Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, USA |
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Abstract: | Recently S. Chmutov introduced a generalization of the dual of a ribbon graph (or equivalently an embedded graph) and proved a relation between Bollobás and Riordan’s ribbon graph polynomial of a ribbon graph and of its generalized duals. Here I show that the duality relation satisfied by the ribbon graph polynomial can be understood in terms of knot theory and I give a simple proof of the relation which used the homfly polynomial of a knot. |
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Keywords: | Bollobá s-Riordan polynomial Duality Graphs on surfaces Homfly polynomial Knots Ribbon graphs Tutte polynomial |
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