Tutte polynomials of fan-like graphs with applications in benzenoid systems

TL;DR

This paper derives formulas for Tutte polynomials of fan-like graphs and applies these results to compute properties like the number of spanning trees in specific benzenoid systems such as pyrene and triphenylene chains.

Contribution

It provides new generating function expressions for Tutte polynomials of fan-like graphs and applies them to benzenoid systems, linking graph theory with chemical structures.

Findings

Explicit Tutte polynomial formulas for fan-like graphs

Number of spanning trees in pyrene and triphenylene chains computed

Applications to chemical graph theory and benzenoid systems

Abstract

We study the computation of the Tutte polynomials of fan-like graphs and obtain expressions of their Tutte polynomials via generating functions. As applications, Tutte polynomials, in particular, the number of spanning trees, of two kinds of benzenoid systems, i.e. pyrene chains and triphenylene chains, are obtained.