Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE RICCI CURVATURE ON DIRECTED GRAPHS

  • Received : 2018.02.08
  • Accepted : 2018.04.10
  • Published : 2019.01.01
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Abstract

In this paper, we consider the Ricci curvature of a directed graph, based on Lin-Lu-Yau's definition. We give some properties of the Ricci curvature, including conditions for a directed regular graph to be Ricci-flat. Moreover, we calculate the Ricci curvature of the cartesian product of directed graphs.

Keywords

DBSHBB_2019_v56n1_113_f0001.png 이미지

FIGURE 1. Complete graph K5, directed cycle C5, and regulartree T3

DBSHBB_2019_v56n1_113_f0002.png 이미지

FIGURE 2. Ladder graph

DBSHBB_2019_v56n1_113_f0003.png 이미지

FIGURE 3. Example of Remark 4.5 and Remark 4.6

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