%0 Journal Article
%T The Tutte Polynomial of Some Matroids
%A Criel Merino
%A Marcelino Ram¨ªrez-Ib¨¢£¿ez
%A Guadalupe Rodr¨ªguez-S¨¢nchez
%J International Journal of Combinatorics
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/430859
%X The Tutte polynomial of a graph or a matroid, named after W. T. Tutte, has the important universal property that essentially any multiplicative graph or network invariant with a deletion and contraction reduction must be an evaluation of it. The deletion and contraction operations are natural reductions for many network models arising from a wide range of problems at the heart of computer science, engineering, optimization, physics, and biology. Even though the invariant is #P-hard to compute in general, there are many occasions when we face the task of computing the Tutte polynomial for some families of graphs or matroids. In this work, we compile known formulas for the Tutte polynomial of some families of graphs and matroids. Also, we give brief explanations of the techniques that were used to find the formulas. Hopefully, this will be useful for researchers in Combinatorics and elsewhere. 1. Introduction Many times, as researchers in Combinatorics, we face the task of computing an evaluation of the Tutte polynomial of a family of graphs or matroids. Sometimes this is not an easy task or at least time consuming. Later, not surprisingly, we find out that a formula was known for a class of graphs or matroids that contains our family. Here we survey some of the best known formulas for some interesting families of graphs and matroids. Our hope is for researchers to have a place to look for a Tutte polynomial before engaging in the search for the Tutte polynomial formula for the considered family. We present along with the formulas, some explanation of the techniques used to compute them. This may also provide tools for computing the Tutte polynomials of new families of graphs or matroids. This survey can also be considered a companion [1]. There, the authors give an introduction of the Tutte polynomial for a general audience of scientists, pointing out relevant relations between different areas of knowledge. But very few explicit calculations are made. Here we consider the practical side of computing the Tutte polynomial. However, we are not presenting evaluations, that are an immense area of research for the Tutte polynomial, nor analysing the complexity of computing the invariant for the different families. For the former, we strongly recommend the book of Welsh [2], for the latter, we recommend Noble¡¯s book chapter [3]. There are many sources for the theory behind this important invariant. The most useful is definitively Brylawski and Oxley book chapter [4]. We already mentioned [1], which also surveys a variety of information about the Tutte
%U http://www.hindawi.com/journals/ijcom/2012/430859/