SuperNOVA: a novel algorithm for graph automorphism calculations

TL;DR

This paper introduces SuperNOVA, a new algorithm for calculating graph automorphism groups that improves performance on star-configured graphs by simplifying the problem into manageable subproblems.

Contribution

SuperNOVA presents a novel approach to automorphism calculations by effectively handling star configurations, addressing limitations of existing methods like Nauty.

Findings

Improved performance on star graphs

Reduces complex automorphism problems to simpler calculations

Enhances efficiency of graph automorphism group determination

Abstract

The graph isomorphism problem is of practical importance, as well as being a theoretical curiosity in computational complexity theory in that it is not known whether it is $NP$-complete or $P$. However, for many graphs, the problem is tractable, and related to the problem of finding the automorphism group of the graph. Perhaps the most well known state-of-the art implementation for finding the automorphism group is Nauty. However, Nauty is particularly susceptible to poor performance on star configurations, where the spokes of the star are isomorphic with each other. In this work, I present an algorithm that explodes these star configurations, reducing the problem to a sequence of simpler automorphism group calculations.