Tutte polynomials of generalized parallel connections

Tutte Polynomials of Generalized Parallel Connections

We use weighted characteristic polynomials to compute Tutte polynomials of generalized parallel connections in the case in which the simplification of the maximal common restriction of the two constituent matroids is a modular flat of the simplifications of both matroids. In particular, this includes cycle matroids of graphs that are identified along complete subgraphs. We also develop formulas...

Parallel connections and coloured Tutte polynomials

We give formulas for the Tutte polynomials of parallel and series connections of weightedmatroids, generalizing and unifying formulas of Oxley and Welsh (Discrete Math. 109 (1992) 185), Bollobás and Riordan (Comb. Probab. Comput. 8 (1999) 45) and Woodall (Discrete Math. 247 (2002) 201). © 2004 Elsevier B.V. All rights reserved.

Tutte Polynomials of Flower Graphs

Zonotopes, toric arrangements, and generalized Tutte polynomials

We introduce a multiplicity Tutte polynomial M(x, y), which generalizes the ordinary one and has applications to zonotopes and toric arrangements. We prove that M(x, y) satisfies a deletion-restriction recurrence and has positive coefficients. The characteristic polynomial and the Poincaré polynomial of a toric arrangement are shown to be specializations of the associated polynomial M(x, y), li...

Tutte polynomials of wheels via generating functions

We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.