# Topological quantum field theory and polynomial identities for graphs on the torus

## TL;DR

This paper connects topological quantum field theory with graph polynomial evaluations, specifically relating SO(3) trace evaluations to the topological Tutte polynomial, and extends the Tutte golden identity to graphs on the torus.

## Contribution

It introduces a novel relation between TQFT trace evaluations and topological Tutte polynomial evaluations, generalizing the Tutte golden identity for torus graphs.

## Key findings

- Established a relation between SO(3) TQFT trace and topological Tutte polynomial
- Proved a generalized Tutte golden identity for graphs on the torus
- Extended polynomial identities to topologically nontrivial surfaces

## Abstract

We establish a relation between the trace evaluation in SO(3) topological quantum field theory and evaluations of a topological Tutte polynomial. As an application, a generalization of the Tutte golden identity is proved for graphs on the torus.