Bakry-Émery and Ollivier Ricci Curvature of Cayley Graphs
In this article we study two discrete curvature notions, Bakry-Émery curvature and Ollivier Ricci curvature, on Cayley graphs. We introduce Right Angled Artin-Coxeter Hybrids (RAACHs) generalizing Right Angled Artin and Coxeter groups (RAAGs and RACGs) and derive the curvatures of Cayley graphs of certain RAACHs. Moreover, we show for general finitely presented groups $\Gamma = \langle S \, \mid\, R \rangle$ that addition of relators does not lead to a decrease in the weighted curvatures of their Cayley graphs with adapted weighting schemes.
Authors
- Florentin Münch (ORCID: https://orcid.org/0000-0001-6123-9507)
- Norbert Peyerimhoff (ORCID: https://orcid.org/0000-0001-9630-7901)
- D. H. Cushing (ORCID: https://orcid.org/0000-0001-5488-2705)
- Riikka Kangaslampi (ORCID: https://orcid.org/0000-0002-9059-8047)
- Supanat Kamtue (ORCID: https://orcid.org/0000-0001-6442-7757)
- Shiping Liu (ORCID: https://orcid.org/0000-0002-9987-1935)
Institutions
- University of Science and Technology of China (CN)
- Chulalongkorn University (TH)
- Tampere University (FI)
- Durham University (GB)
- University of Manchester (GB)
- Leipzig University (DE)
Publication Details
- Journal
- The Electronic Journal of Combinatorics
- Published
- 2025-08-08
- DOI
- https://doi.org/10.37236/13434
- Primary Topic
- Geometric Analysis and Curvature Flows
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Leverhulme Trust
- National Natural Science Foundation of China
- Tsinghua University