Aut($\Gamma$)=det($M_\Gamma$)

TL;DR

This paper demonstrates that the automorphism group of any hypergraph can be represented as the determinant of a matrix over a specific ring, providing a new method to determine graph isomorphism.

Contribution

It introduces a novel algebraic approach linking hypergraph automorphisms to matrix determinants over rings, enabling graph isomorphism testing.

Findings

Automorphism groups correspond to matrix determinants over rings.

Method allows for graph isomorphism determination.

Provides algebraic tools for hypergraph analysis.

Abstract

In this article, we will show that the automorphism group of any hypergraph is essentially equal to the determinant of some matrix over a ring generated from the set of ground points. With this, we are also able to determine whether two graphs are isomorphic.