Graph isomorphism and automorphism problems are polynomial

TL;DR

This paper presents a polynomial-time algorithm for solving the graph isomorphism and automorphism problems, which are fundamental in various scientific fields and were previously suspected to be NP-complete.

Contribution

The paper introduces a novel polynomial-time algorithm that efficiently solves both graph automorphism and isomorphism problems, challenging prior assumptions about their computational complexity.

Findings

Algorithm solves graph isomorphism and automorphism in polynomial time

Implementation is straightforward and adaptable for various applications

Potential to impact multiple scientific disciplines by enabling efficient graph analysis

Abstract

Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization, computational logic, structure recognition, and dynamics of complex systems. Both problems have previously been suspected, but not proven, to be NP-complete. In this paper we propose an algorithm that solves both graph automorphism and isomorphism problems in polynomial time. The algorithm can be easily implemented and thus opens up a wide range of applications.