Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-23T22:51:45.841Z Has data issue: false hasContentIssue false

11 - Classification of rank 3 graphs

Published online by Cambridge University Press:  06 January 2022

Andries E. Brouwer
Affiliation:
Technische Universiteit Eindhoven, The Netherlands
H. Van Maldeghem
Affiliation:
Universiteit Gent, Belgium
Get access

Summary

The classification of rank 3 graphs is due to Foulser-Kallaher-Kantor-Liebler-Liebeck- Saxl and others. We describe that result in this chapter. We provide the relevant group-theoretic theorems (without proof) and identify all graphs that appear with graphs that were mentioned (and in most cases explicitly constructed) in previous chapters. This way, we give all pairs (Γ,), with Γ a strongly regular graph and 𝐺 a group of automorphisms of Γ acting rank 3. We also provide a table of the parameters of the sporadic rank 3 graphs, which have up to 531441 vertices, and a similar table for all rank 3 graphs up to 1024 vertices. Finally, we tabulate small primitive rank 4–10 strongly regular graphs which do not have Latin square parameters.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×