RICCI CURVATURE, CIRCULANTS, AND EXTENDED MATCHING CONDITIONS

Abstract

Ricci curvature for locally finite graphs, as proposed by Lin, Lu and Yau, provides a useful isomorphism invariant. A Matching Condition was introduced as a key tool for computation of this Ricci curvature. The scope of the Matching Condition is quite broad, but it does not cover all cases. Thus the current paper introduces extended versions of the Matching Condition, and applies them to the computation of the Ricci curvature of a class of circulants determined by certain number-theoretic data. The classical Matching Condition is also applied to determine the Ricci curvature for other families of circulants, along with Cayley graphs of abelian groups that are generated by the complements of (unions of) subgroups.