# The Graph Curvature Calculator and the Curvatures of Cubic Graphs

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**The Graph Curvature Calculator and the Curvatures of Cubic Graphs.** / Cushing, David; Kangaslampi, Riikka; Lipiäinen, Valtteri; Liu, Shiping; Stagg, George W.

Research output: Contribution to journal › Article › Scientific › peer-review

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*Experimental Mathematics*. https://doi.org/10.1080/10586458.2019.1660740

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*Experimental Mathematics*. https://doi.org/10.1080/10586458.2019.1660740

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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 - 2019/1/1

Y1 - 2019/1/1

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. 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.

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. 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.

KW - cubic graph

KW - discrete curvature

KW - expander graph

KW - Graph Curvature Calculator

KW - graph theory

UR - http://www.scopus.com/inward/record.url?scp=85073832072&partnerID=8YFLogxK

U2 - 10.1080/10586458.2019.1660740

DO - 10.1080/10586458.2019.1660740

M3 - Article

AN - SCOPUS:85073832072

JO - Experimental Mathematics

JF - Experimental Mathematics

SN - 1058-6458

ER -

ID: 38810417