Betti numbers of unordered configuration spaces of small graphs

TL;DR

This paper compiles known Betti numbers for unordered configuration spaces of small, simple graphs to assist researchers and prevent redundant calculations.

Contribution

It provides a comprehensive dataset of Betti numbers for specific small graphs, aiding future topological and combinatorial research.

Findings

Data covers connected multigraphs with up to nine edges

Graphs have no loops, bivalent vertices, or internal bridges

Serves as a reference for Betti numbers in topological graph studies

Abstract

The purpose of this document is to provide data about known Betti numbers of unordered configuration spaces of small graphs in order to guide research and avoid duplicated effort. It contains information for connected multigraphs having at most nine edges which contain no loops, no bivalent vertices, and no internal (i.e., non-leaf) bridges.