The Tutte polynomial of a graph, depth-first search, and simplicial complex partitions

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.

Vertex Decomposable Simplicial Complexes Associated to Path Graphs

Introduction Vertex decomposability of a simplicial complex is a combinatorial topological concept which is related to the algebraic properties of the Stanley-Reisner ring of the simplicial complex. This notion was first defined by Provan and Billera in 1980 for k-decomposable pure complexes which is known as vertex decomposable when . Later Bjorner and Wachs extended this concept to non-pure ...

Knots and Graphs

A classical matrix-tree theorem expresses the determinant of some matrix constructed from a graph (principal minor of the Laplacian) as a sum over all spanning trees of the graph. There are generalizations of this theorem to hypergraphs or simplicial complexes [MV, DKM]. Some version of this theorem provides a formula for the first non-zero coefficient of the Conway polynomial of a (virtual) li...

Tutte Polynomials of Flower Graphs

Computing the Invariant Polynomials of Graphs, Networks and Matroids

The invariant polynomials of discrete systems such as graphs, matroids, hyperplane arrangements, and simplicial complexes, have been theoretically investigated actively in recent years. These invariants include the Tutte polynomial of a graph and a matroid, the chromatic polynomial of a graph, the network reliability of a network, the Jones polynomial of a link, the percolation function of a gr...