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We show how the results of Brylawski and Oxley [4] on the Tutte polynomial of a tensor product of graphs may be generalized to colored graphs and the Tutte polynomials introduced by Bollobás and Riordan [1]. This is a generalization of our earlier work on signed graphs with applications to knot theory. Our result makes the calculation of certain invariants… (More)

We provide a new proof of Brylawski's formula for the Tutte polynomial of the tensor product of two matroids. Our proof involves extending Tutte's formula, expressing the Tutte polynomial using a calculus of activities, to all polynomials involved in Brylawski's formula. The approach presented here may be used to show a signed generalization of Brylawski's… (More)

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