Tutte uniqueness of line graphs

On Tutte polynomial uniqueness of twisted wheels

A graph G is called T -unique if any other graph having the same Tutte polynomial as G is isomorphic to G. Recently, there has been much interest in determining T -unique graphs and matroids. For example, de Mier and Noy [A. de Mier, M. Noy, On graphs determined by their Tutte polynomials, Graphs Combin. 20 (2004) 105–119; A. de Mier, M. Noy, Tutte uniqueness of line graphs, Discrete Math. 301 ...

Tutte Polynomials of Flower Graphs

Homomorphisms and Polynomial Invariants of Graphs

This paper initiates a study of the connection between graph homomorphisms and the Tutte polynomial. This connection enables us to extend the study to other important polynomial invariants associated with graphs, and closely related to the Tutte polynomial. We then obtain applications of these relationships in several areas, including Abelian Groups and Statistical Physics. A new type of unique...

Hexagonal Tilings and Locally C6 Graphs

We give a complete classification of hexagonal tilings and locally C6 graphs, by showing that each of them has a natural embedding in the torus or in the Klein bottle (see [12]). We also show that locally grid graphs, defined in [9, 12], are minors of hexagonal tilings (and by duality of locally C6 graphs) by contraction of a particular perfect matching and deletion of the resulting parallel ed...

On the Structure of Graphs Which Are Locally Indistinguishable from a Lattice

For each integer d > 3, we obtain a characterization of all graphs in which the ball of radius 3 around each vertex is isomorphic to the ball of radius 3 in Ld , the graph of the d-dimensional integer lattice. The finite, connected graphs with this property have a highly rigid, ‘global’ algebraic structure; they can be viewed as quotient lattices of Ld in various compact d-dimensional orbifolds...