Geodesic
Bakry-Émery and Ollivier Ricci curvature of Cayley graphs
David Cushing1 ; Supanat Kamtue2 ; Riikka Kangaslampi3 ; Shiping Liu4 ; Florentin Münch5 ; Norbert Peyerimhoff6
1The University of Manchester
2Chulalongkorn University
3Tampere University
4University of Science and Technology of China
5Leipzig University
6Durham University
The electronic journal of combinatorics, Tome 32 (2025) no. 3
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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.
DOI : 10.37236/13434
Classification : 05C50, 53A70

David Cushing  1   ; Supanat Kamtue  2   ; Riikka Kangaslampi  3   ; Shiping Liu  4   ; Florentin Münch  5   ; Norbert Peyerimhoff  6

1 The University of Manchester
2 Chulalongkorn University
3 Tampere University
4 University of Science and Technology of China
5 Leipzig University
6 Durham University 
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     author = {David Cushing and Supanat Kamtue and Riikka Kangaslampi and Shiping Liu and Florentin M\"unch and Norbert Peyerimhoff},
     title = {Bakry-\'Emery and {Ollivier} {Ricci} curvature of {Cayley} graphs},
     journal = {The electronic journal of combinatorics},
     year = {2025},
     volume = {32},
     number = {3},
     doi = {10.37236/13434},
     zbl = {8097649},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/13434/}
}
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David Cushing; Supanat Kamtue; Riikka Kangaslampi; Shiping Liu; Florentin Münch; Norbert Peyerimhoff. Bakry-Émery and Ollivier Ricci curvature of Cayley graphs. The electronic journal of combinatorics, Tome 32 (2025) no. 3. doi: 10.37236/13434

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