Parametrized Tutte Polynomials of Graphs and Matroids

Tutte Polynomials of Flower Graphs

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...

Tutte-martin polynomials and orienting vectors of isotropic systems

Isotropic systems are structures which unify some properties of 4-regular graphs and of pairs of dual binary matroids. In this paper we unify the properties of the symmetric Tutte polynomials (i.e. with equal variables) of binary matroids and of the Martin polynomials of 4-regular graphs. For this purpose we introduce the orienting vectors of an isotropic system in order to generalize the euler...

Strong Tutte Functions of Matroids and Graphs

A strong Tutte function of matroids is a function of finite matroids which satisfies F ( M 1$M2) = F ( M 1 ) F ( M 2 ) and F ( M ) = aeF(M\e) + b e F ( M / e ) for e not a loop or coloop of M ,where ae , be are scalar parameters depending only on e . We classify strong Tutte functions of all matroids into seven types, generalizing Brylawski's classification of Tutte-Grothendieck invariants. One...

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

It 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 simp...