Bull. Korean Math. Soc. 2019; 56(1): 201-217
Online first article July 4, 2018 Printed January 31, 2019
https://doi.org/10.4134/BKMS.b180179
Copyright © The Korean Mathematical Society.
Mehmet Da\v{g}l{\i}, Oktay Olmez, Jonathan D. H. Smith
Amasya University; Ankara University; Iowa State University
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.
Keywords: Ricci curvature, Matching Condition, circulant graph, Cayley graph
MSC numbers: 05C10, 05C81
2020; 57(2): 295-309
2019; 56(4): 841-852
2017; 54(3): 967-973
2016; 53(4): 1017-1031
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