A Family of Counter Examples to an Approach to Graph Isomorphism

TL;DR

This paper presents a family of counterexamples that challenge a recent approach to solving the graph isomorphism problem using specific polytopes, highlighting limitations in Friedland's proposed method.

Contribution

It introduces a new family of counterexamples demonstrating that two sequences of polytopes differ, undermining a proposed polynomial-time graph isomorphism algorithm.

Findings

The polytopes $\

,

$ differ for the constructed counterexamples.

Abstract

We give a family of counter examples showing that the two sequences of polytopes $\Phi_{n,n}$ and $\Psi_{n,n}$ are different. These polytopes were defined recently by S. Friedland in an attempt at a polynomial time algorithm for graph isomorphism.