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
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