Ricci-flat cubic graphs with girth five

David  Cushing; Riikka Kangaslampi; Yong Lin; Shiping Liu; Linyuan Lu; Shing-Tung Yau

doi:10.4310/CAG.2021.v29.n7.a3

Ricci-flat cubic graphs with girth five

David Cushing, Riikka Kangaslampi, Yong Lin, Shiping Liu, Linyuan Lu, Shing-Tung Yau

Tietotekniikka

Tutkimustuotos: Artikkeli › Scientific › vertaisarvioitu

Abstrakti

We classify all connected, simple, 3-regular graphs with girth at least 5 that are Ricci-flat. We use the definition of Ricci curvature on graphs given in Lin-Lu-Yau, Tohoku Math., 2011, which is a variation of Ollivier, J. Funct. Anal., 2009. A graph is Ricci-flat, if it has vanishing Ricci curvature on all edges. We show, that the only Ricci-flat cubic graphs with girth at least 5 are the Petersen graph, the Triplex and the dodecahedral graph. This will correct the classification in Lin-Lu-Yau, Comm. Anal. Geom., 2014, that misses the Triplex.

Alkuperäiskieli	Englanti
Sivut	1559–1570
Julkaisu	COMMUNICATIONS IN ANALYSIS AND GEOMETRY
Vuosikerta	29
Numero	7
DOI - pysyväislinkit	https://doi.org/10.4310/CAG.2021.v29.n7.a3
Tila	Julkaistu - toukok. 2022
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Julkaisufoorumi-taso

Jufo-taso 2

Pääsy asiakirjaan

10.4310/CAG.2021.v29.n7.a3

cubic_girth5_2
This publication is copyrighted. You may download, display and print it for Your own personal use. Commercial use is prohibited.
Accepted author manuscript, 261 KBLisenssi: Unspecified

https://urn.fi/URN:NBN:fi:tuni-202209026865

Muut tiedostot ja linkit

https://doi.org/10.48550/arXiv.1802.02982

Siteeraa tätä

@article{abfa9bb776e84e389cf1b4ea64c35101,

title = "Ricci-flat cubic graphs with girth five",

abstract = "We classify all connected, simple, 3-regular graphs with girth at least 5 that are Ricci-flat. We use the definition of Ricci curvature on graphs given in Lin-Lu-Yau, Tohoku Math., 2011, which is a variation of Ollivier, J. Funct. Anal., 2009. A graph is Ricci-flat, if it has vanishing Ricci curvature on all edges. We show, that the only Ricci-flat cubic graphs with girth at least 5 are the Petersen graph, the Triplex and the dodecahedral graph. This will correct the classification in Lin-Lu-Yau, Comm. Anal. Geom., 2014, that misses the Triplex.",

author = "David Cushing and Riikka Kangaslampi and Yong Lin and Shiping Liu and Linyuan Lu and Shing-Tung Yau",

year = "2022",

month = may,

doi = "10.4310/CAG.2021.v29.n7.a3",

language = "English",

volume = "29",

pages = "1559–1570",

journal = "COMMUNICATIONS IN ANALYSIS AND GEOMETRY",

issn = "1019-8385",

number = "7",

}

TY - JOUR

T1 - Ricci-flat cubic graphs with girth five

AU - Cushing, David

AU - Kangaslampi, Riikka

AU - Lin, Yong

AU - Liu, Shiping

AU - Lu, Linyuan

AU - Yau, Shing-Tung

PY - 2022/5

Y1 - 2022/5

N2 - We classify all connected, simple, 3-regular graphs with girth at least 5 that are Ricci-flat. We use the definition of Ricci curvature on graphs given in Lin-Lu-Yau, Tohoku Math., 2011, which is a variation of Ollivier, J. Funct. Anal., 2009. A graph is Ricci-flat, if it has vanishing Ricci curvature on all edges. We show, that the only Ricci-flat cubic graphs with girth at least 5 are the Petersen graph, the Triplex and the dodecahedral graph. This will correct the classification in Lin-Lu-Yau, Comm. Anal. Geom., 2014, that misses the Triplex.

AB - We classify all connected, simple, 3-regular graphs with girth at least 5 that are Ricci-flat. We use the definition of Ricci curvature on graphs given in Lin-Lu-Yau, Tohoku Math., 2011, which is a variation of Ollivier, J. Funct. Anal., 2009. A graph is Ricci-flat, if it has vanishing Ricci curvature on all edges. We show, that the only Ricci-flat cubic graphs with girth at least 5 are the Petersen graph, the Triplex and the dodecahedral graph. This will correct the classification in Lin-Lu-Yau, Comm. Anal. Geom., 2014, that misses the Triplex.

UR - https://doi.org/10.48550/arXiv.1802.02982

U2 - 10.4310/CAG.2021.v29.n7.a3

DO - 10.4310/CAG.2021.v29.n7.a3

M3 - Article

VL - 29

SP - 1559

EP - 1570

JO - COMMUNICATIONS IN ANALYSIS AND GEOMETRY

JF - COMMUNICATIONS IN ANALYSIS AND GEOMETRY

SN - 1019-8385

IS - 7

ER -

Ricci-flat cubic graphs with girth five

Abstrakti

Julkaisufoorumi-taso

Pääsy asiakirjaan

Muut tiedostot ja linkit

Sormenjälki

Siteeraa tätä