On the graph isomorphism problem

TL;DR

This paper explores the relationship between the graph isomorphism problem and the solvability of specific linear systems with nonnegative variables, offering a new perspective on this computational challenge.

Contribution

It introduces a novel approach linking graph isomorphism to linear algebraic systems, providing insights into the problem's structure.

Findings

Establishes a connection between graph isomorphism and linear systems.

Replaces previous versions with updated insights.

Provides a new framework for analyzing graph isomorphism.

Abstract

We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.