Implementing Brouwer's database of strongly regular graphs

TL;DR

This paper details the implementation of Brouwer's database of strongly regular graphs within Sagemath, enabling verification and extension of known existence results for graphs with up to 1300 vertices.

Contribution

The authors implemented most infinite families and sporadic cases of strongly regular graphs in Sagemath, expanding the database and providing concrete graph constructions.

Findings

Successfully implemented many infinite families of graphs

Constructed examples for sporadic parameter cases

Extended the database to higher vertex counts

Abstract

Andries Brouwer maintains a public database of existence results for strongly regular graphs on $n\leq 1300$ vertices. We implemented most of the infinite families of graphs listed there in the open-source software Sagemath, as well as provided constructions of the "sporadic" cases, to obtain a graph for each set of parameters with known examples. Besides providing a convenient way to verify these existence results from the actual graphs, it also extends the database to higher values of $n$.