대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제56권1호
  • /
  • Pages.201-217
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  • 2019
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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RICCI CURVATURE, CIRCULANTS, AND EXTENDED MATCHING CONDITIONS

  • Dagli, Mehmet (Department of Mathematics Amasya University) ;
  • Olmez, Oktay (Department of Mathematics Amasya University) ;
  • Smith, Jonathan D.H. (Department of Mathematics Iowa State University)
  • 투고 : 2018.02.28
  • 심사 : 2018.06.07
  • 발행 : 2019.01.31
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초록

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

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  7. J. D. H. Smith, Ricci curvature, circulants, and a matching condition, Discrete Math. 329 (2014), 88-98. https://doi.org/10.1016/j.disc.2014.04.010