# A Note on Using the Resistance-Distance Matrix to solve Hamiltonian Cycle Problem

## TL;DR

This paper explores using resistance distance and its inverse as edge weights in converting Hamiltonian cycle problems to TSP instances, showing improved performance on difficult cases.

## Contribution

It introduces resistance distance-based weighting strategies for TSP conversions of Hamiltonian cycle problems, demonstrating their effectiveness on challenging instances.

## Key findings

- Resistance distance improves TSP solution quality for hard instances.
- Inverse resistance distance yields even stronger performance.
- Examples show clear benefits of these weighting choices.

## Abstract

An instance of Hamiltonian cycle problem can be solved by converting it to an instance of Travelling salesman problem, assigning any choice of weights to edges of the underlying graph. In this note we demonstrate that, for difficult instances, choosing the edge weights to be the resistance distance between its two incident vertices is often a good choice. We also demonstrate that arguably stronger performance arises from using the inverse of the resistance distance. Examples are provided demonstrating benefits gained from these choices.