tutte polynomials of flower graphs

Tutte Polynomials of Flower Graphs

Tutte Polynomials for Directed Graphs

The Tutte polynomial is a fundamental invariant of graphs. In this article, we define and study a generalization of the Tutte polynomial for directed graphs, that we name B-polynomial. The B-polynomial has three variables, but when specialized to the case of graphs (that is, digraphs where arcs come in pairs with opposite directions), one of the variables becomes redundant and the B-polynomial ...

Parametrized Tutte Polynomials of Graphs and Matroids

We generalize and unify results on parametrized and coloured Tutte polynomials of graphs and matroids due to Zaslavsky, and Bollobás and Riordan. We give a generalized Zaslavsky– Bollobás–Riordan theorem that characterizes parametrized contraction–deletion functions on minor-closed classes of matroids, as well as the modifications necessary to apply the discussion to classes of graphs. In gener...

Chromatic and Tutte Polynomials for Graphs, Rooted Graphs and Trees

The chromatic polynomial of a graph is a one-variable polynomial that counts the number of ways the vertices of a graph can be properly colored. It was invented in 1912 by G.D. Birkhoff in his unsuccessful attempt to solve the four-color problem. In the 1940’s, Tutte generalized Birkhoff’s polynomial by adding another variable and analyzing its combinatorial properties. The Tutte polynomial its...

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.

Chain polynomials and Tutte polynomials

The recently introduced chain and sheaf polynomials of a graph are shown to be essentially equivalent to a weighted version of the Tutte polynomial. c © 2002 Elsevier Science B.V. All rights reserved.