The Graph Curvature Calculator and the Curvatures of Cubic Graphs

David Cushing, Riikka Kangaslampi*, Valtteri Lipiäinen, Shiping Liu, George W. Stagg

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)

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.

Original languageEnglish
JournalExperimental Mathematics
DOIs
Publication statusPublished - 1 Jan 2019
MoE publication typeA1 Journal article-refereed

Keywords

  • cubic graph
  • discrete curvature
  • expander graph
  • Graph Curvature Calculator
  • graph theory

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