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.

In: Experimental Mathematics, 14.09.2019.

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

Author

Cushing, David ; Kangaslampi, Riikka ; Lipiäinen, Valtteri ; Liu, Shiping ; Stagg, George W. / The Graph Curvature Calculator and the curvatures of cubic graphs. In: Experimental Mathematics. 2019.

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@article{d637448770924f33af5550712d71eed0,

title = "The Graph Curvature Calculator and the curvatures of cubic graphs",

abstract = "We classify all cubic graphs with either non-negative Ollivier-Ricci curvature or non-negative Bakry-{\'E}mery curvature everywhere. We show in both curvature notions that the non-negatively curved graphs are the prism graphs and the M{\"o}bius 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.",

author = "David Cushing and Riikka Kangaslampi and Valtteri Lipi{\"a}inen and Shiping Liu and Stagg, {George W.}",

year = "2019",

month = "9",

day = "14",

doi = "10.1080/10586458.2019.1660740",

language = "English",

journal = "Experimental Mathematics",

issn = "1058-6458",

publisher = "Taylor & Francis",

}

RIS (suitable for import to EndNote) - Download

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 -

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