The Graph Curvature Calculator and the Curvatures of Cubic Graphs. Issue 2 (27th July 2022)

• Record Type: Journal Article
• Authors: Cushing, David; Kangaslampi, Riikka; Lipiäinen, Valtteri; Liu, Shiping; Stagg, George W.
• Is Part Of: Experimental mathematics. Volume 31:Issue 2(2022)
• Page Start: 583
• Page End: 595
• Publication Date: 2022-07-27
• Subjects: discrete curvature -- graph theory -- cubic graph -- expander graph -- Graph Curvature Calculator; Primary 05C50 -- Secondary 39A12, 51K10; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2019.1660740
• Languages: English
• ISSNs: 1058-6458

Abstract

Abstract: We classify all cubic graphs with either non-negative Ollivier-Ricci curvature or non-negative Bakry-Émery curvature everywhere. We show in both curvature notions that the non-negatively curved graphs are the prism graphs and the Möbius ladders. As a consequence of the classification result we show that non-negatively curved cubic expanders do not exist. We also introduce the Graph Curvature Calculator, an online tool developed for calculating the curvature of graphs under several variants of the curvature notions that we use in the classification.