Vol. 13, No. 4, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 3, 361–540
Issue 2, 181–360
Issue 1, 1–179

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Author Index
Coming Soon
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Condensed Ricci curvature of complete and strongly regular graphs

Vincent Bonini, Conor Carroll, Uyen Dinh, Sydney Dye, Joshua Frederick and Erin Pearse

Vol. 13 (2020), No. 4, 559–576
Abstract

We study a modified notion of Ollivier’s coarse Ricci curvature on graphs introduced by Lin, Lu, and Yau. We establish a rigidity theorem for complete graphs that shows a connected finite simple graph is complete if and only if the Ricci curvature is strictly greater than 1. We then derive explicit Ricci curvature formulas for strongly regular graphs in terms of the graph parameters and the size of a maximal matching in the core neighborhood. As a consequence we are able to derive exact Ricci curvature formulas for strongly regular graphs of girths 4 and 5 using elementary means. An example is provided that shows there is no exact formula for the Ricci curvature for strongly regular graphs of girth 3 that is purely in terms of graph parameters.

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/involve

We have not been able to recognize your IP address 3.215.177.171 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 30.00:

Keywords
coarse Ricci curvature, strongly regular graphs
Mathematical Subject Classification 2010
Primary: 52C99, 53B99
Secondary: 05C10, 05C81, 05C99
Milestones
Received: 26 August 2019
Revised: 11 March 2020
Accepted: 6 August 2020
Published: 20 November 2020

Communicated by Kenneth S. Berenhaut
Authors
Vincent Bonini
Mathematics Department
California Polytechnic State University
San Luis Obispo, CA
United States
Conor Carroll
Mathematics Department
California Polytechnic State University
San Luis Obispo, CA
United States
Uyen Dinh
Mathematics Department
California Polytechnic State University
San Luis Obispo, CA
United States
Sydney Dye
Mathematics Department
California Polytechnic State University
San Luis Obispo, CA
United States
Joshua Frederick
Mathematics Department
California Polytechnic State University
San Luis Obispo, CA
United States
Erin Pearse
Mathematics Department
California Polytechnic State University
San Luis Obispo, CA
United States