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Relative Tutte Polynomials of Tensor Products of Coloured Graphs

Published online by Cambridge University Press:  04 September 2013

Y. DIAO  and
G. HETYEI
Y. DIAO
Affiliation:
Department of Mathematics and Statistics, UNC Charlotte, Charlotte, NC 28223, USA (e-mail: ydiao@uncc.edu, ghetyei@uncc.edu)
G. HETYEI
Affiliation:
Department of Mathematics and Statistics, UNC Charlotte, Charlotte, NC 28223, USA (e-mail: ydiao@uncc.edu, ghetyei@uncc.edu)
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Abstract

The tensor product (G1,G2) of a graph G1 and a pointed graph G2 (containing one distinguished edge) is obtained by identifying each edge of G1 with the distinguished edge of a separate copy of G2, and then removing the identified edges. A formula to compute the Tutte polynomial of a tensor product of graphs was originally given by Brylawski. This formula was recently generalized to coloured graphs and the generalized Tutte polynomial introduced by Bollobás and Riordan. In this paper we generalize the coloured tensor product formula to relative Tutte polynomials of relative graphs, containing zero edges to which the usual deletion/contraction rules do not apply. As we have shown in a recent paper, relative Tutte polynomials may be used to compute the Jones polynomial of a virtual knot.

Keywords

Primary 05C35Secondary 05C1557M25
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 22 , Issue 6 , November 2013 , pp. 801 - 828
Copyright
Copyright © Cambridge University Press 2013 

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