String representation of trivalent 2-stratifolds with trivial fundamental group

TL;DR

This paper presents a Python algorithm that efficiently generates all distinct trivalent 2-stratifold graphs with trivial fundamental group up to a specified number of white vertices, utilizing graph automorphism recognition and isomorphism detection.

Contribution

The paper introduces a novel Python program that constructs and identifies unique trivalent 2-stratifold graphs using optimized graph automorphism and isomorphism algorithms.

Findings

Efficient enumeration of all distinct graphs up to N white vertices.

Use of automorphism recognition to reduce redundant graph generation.

Linear-time isomorphism detection via a variation of the AHU algorithm.

Abstract

We give a Python program that is capable to compute and print all the distinct trivalent 2-stratifold graphs up to $N$ white vertices with trivial fundamental group. Our algorithm uses the three basic operations to construct new graphs from any set of given graphs. We iterate this process to construct all the desired graphs. The algorithm includes an optimization that reduces the repetition of generated graphs, this is done by recognizing equivalent white vertices of a graph under automorphism. We use a variation of the AHU algorithm to identify those vertices and as well to distinguish isomorphic graphs in linear time. The returned string from the AHU algorithm is also used as a hashing function to search for repeated graphs in amortized constant time.