The Twist Numbers of Graphs and the Tutte Polynomial

Tutte Polynomials of Flower Graphs

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.

Bell and Stirling Numbers for Graphs

The Bell number B(G) of a simple graph G is the number of partitions of its vertex set whose blocks are independent sets of G. The number of these partitions with k blocks is the (graphical) Stirling number S(G, k) of G. We explore integer sequences of Bell numbers for various one-parameter families of graphs, generalizations of the relation B(Pn) = B(En−1) for path and edgeless graphs, one-par...

Twisted Duality and Polynomials of Embedded Graphs

We consider two operations on the edge of an embedded graph (or equivalently a ribbon graph): giving a half-twist to the edge and taking the partial dual with respect to the edge. These two operations give rise to an action of S3 e(G), the ribbon group of G, on G. We show that this ribbon group action gives a complete characterization of duality in that if G is any cellularly embedded graph wit...