This analysis reveals properties of bakry-émery and ollivier ricci curvature in cayley graphs, indicating group structure influences curvature outcomes.
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 Γ = S \, \, R that addition of relators does not lead to a decrease in the weighted curvatures of their Cayley graphs with adapted weighting schemes.
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Cushing et al. (2025) studied this question.
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