Polynomial time randomised approxmiation schemes for the Tutte polynomial of dense graphs

Tutte Polynomials of Flower Graphs

Polynomial time randomised approximation schemes for the Tutte polynomial of dense graphs - Foundations of Computer Science, 1994 Proceedings., 35th Annual Symposium on

The Tutte-Gr6thendieck polynomial T(G; x, y) of a graph G encodes numerous interesting combinatorial quantities associated with the graph. Its evaluation in various points in the (x,y) plane give the number of spanning forests of the graph, the number of its strongly connected orientations, the number of its proper k-colorings, the (all terminal) reliability probability of the graph, and variou...

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.

On the tutte polynomial of benzenoid chains

The Tutte polynomial of a graph G, T(G, x,y) is a polynomial in two variables defined for every undirected graph contains information about how the graph is connected. In this paper a simple formula for computing Tutte polynomial of a benzenoid chain is presented.

Polynomial time randomised approximation schemes for Tutte-Gröthendieck invariants: the dense case

The Tutte-Gröthendieck polynomial T (G;x, y) of a graph G encodes numerous interesting combinatorial quantities associated with the graph. Its evaluation in various points in the (x, y) plane give the number of spanning forests of the graph, the number of its strongly connected orientations, the number of its proper k-colorings, the (all terminal) reliability probability of the graph, and vario...