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2020 Condensed Ricci curvature of complete and strongly regular graphs
Vincent Bonini, Conor Carroll, Uyen Dinh, Sydney Dye, Joshua Frederick, Erin Pearse
Involve 13(4): 559-576 (2020). DOI: 10.2140/involve.2020.13.559

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.

Citation

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Vincent Bonini. Conor Carroll. Uyen Dinh. Sydney Dye. Joshua Frederick. Erin Pearse. "Condensed Ricci curvature of complete and strongly regular graphs." Involve 13 (4) 559 - 576, 2020. https://doi.org/10.2140/involve.2020.13.559

Information

Received: 26 August 2019; Revised: 11 March 2020; Accepted: 6 August 2020; Published: 2020
First available in Project Euclid: 22 December 2020

MathSciNet: MR4190424
Digital Object Identifier: 10.2140/involve.2020.13.559

Subjects:
Primary: 52C99, 53B99
Secondary: 05C10, 05C81, 05C99

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 4 • 2020
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