The Number of 0-1-2 Increasing Trees as Two Different Evaluations of the Tutte Polynomial of a Complete Graph

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.

Combinatorial evaluations of the Tutte polynomial

The Tutte polynomial is one of the most important and most useful invariants of a graph. It was discovered as a two variable generalization of the chromatic polynomial [15, 16], and has been studied in literally hundreds of papers, in part due to its connections to various fields ranging from Enumerative Combinatorics to Knot Theory, from Statistical Physics to Computer Science. We refer the re...

Edge-Selection Heuristics for Computing Tutte Polynomials

The Tutte polynomial of a graph, also known as the partition function of the q-state Potts model, is a 2-variable polynomial graph invariant of considerable importance in both combinatorics and statistical physics. It contains several other polynomial invariants, such as the chromatic polynomial and flow polynomial as partial evaluations, and various numerical invariants, such as the number of ...

Tutte Polynomials of Flower Graphs

Increasing trees and alternating permutations

In this article we consider some increasing trees, the number of which is equal to the number of alternating (updown) permutations, that is, permutations of the form σ(1) < σ(2) > σ(3) < ... . It turns out that there are several such classes of increasing trees, each of which is interesting in itself. Special attention is paid to the study of various statistics on these trees, connected with th...