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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.
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참고문헌 (7)
참고문헌 신청
B. B. Bhattacharya / 2015 / Exact and asymptotic results on coarse Ricci curvature of graphs / Discrete Math 338(1):23~42
D. P. Bourne / 2017 / Ollivier-Ricci idleness functions of graphs / arXiv:1704.04398v2 [math.CO]
G. H. Hardy / 1960 / The Theory of Numbers / Oxford University Press
Y. Lin / 2011 / Ricci curvature of graphs / Tohoku Math. J. (2) 63(4):605~627
Y. Lin / 2014 / Ricci-at graphs with girth at least ve / Comm. Anal. Geom 22(4):671~687
D. P. Bourne / 2017 / Ollivier-Ricci idleness functions of graphs / arXiv:1704.04398v2 [math.CO]
G. H. Hardy / 1960 / The Theory of Numbers / Oxford University Press
Y. Lin / 2011 / Ricci curvature of graphs / Tohoku Math. J. (2) 63(4):605~627
Y. Lin / 2014 / Ricci-at graphs with girth at least ve / Comm. Anal. Geom 22(4):671~687
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