TY - JOUR
T1 - The Graph Curvature Calculator and the curvatures of cubic graphs
AU - Cushing, David
AU - Kangaslampi, Riikka
AU - Lipiäinen, Valtteri
AU - Liu, Shiping
AU - Stagg, George W.
PY - 2019/9/14
Y1 - 2019/9/14
N2 - 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. We also highlight an online tool for calculating the curvature of graphs under several variants of these curvature notions that we use in the classification. As a consequence of the classification result we show, that non-negatively curved cubic expanders do not exist.
AB - 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. We also highlight an online tool for calculating the curvature of graphs under several variants of these curvature notions that we use in the classification. As a consequence of the classification result we show, that non-negatively curved cubic expanders do not exist.
U2 - 10.1080/10586458.2019.1660740
DO - 10.1080/10586458.2019.1660740
M3 - Article
JO - Experimental Mathematics
JF - Experimental Mathematics
SN - 1058-6458
ER -