Polynomial Time Symmetry and Isomorphism Testing for Connected Graphs

TL;DR

This paper introduces a polynomial-time method for testing symmetry and isomorphism in connected graphs using Kirchhoff resistor networks, leading to canonical labelings of graph nodes and edges.

Contribution

It presents a novel approach leveraging resistor networks to efficiently produce canonical labelings for connected graphs.

Findings

Polynomial-time symmetry testing for connected graphs

Canonical labelings of nodes and edges achieved

Resistor network approach effective for graph isomorphism

Abstract

We use the concept of a Kirchhoff resistor network (alternatively random walk on a network) to probe connected graphs and produce symmetry revealing canonical labelings of the graph(s) nodes and edges.