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Ricci-flat Graphs with Girth Four

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Abstract

Lin-Lu-Yau introduced a notion of Ricci curvature for graphs and obtained a complete classification for all Ricci-flat graphs with girth at least five. In this paper, we characterize all Ricci-flat graphs of girth four with vertex-disjoint 4-cycles.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou, 510520, P. R. China

    Wei Hua He

  2. School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, P. R. China

    Jun Luo

  3. School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou, 510006, P. R. China

    Chao Yang

  4. School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, P. R. China

    Wei Yuan & Hui Chun Zhang

Authors
  1. Wei Hua He
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  2. Jun Luo
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  3. Chao Yang
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  4. Wei Yuan
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  5. Hui Chun Zhang
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Corresponding author

Correspondence to Chao Yang.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 11601093, 12025109, 12071489 and 61976104) and the Research Fund of Guangdong University of Foreign Studies (Grant Nos. 299-X5219228 and 297-ZW200011)

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He, W.H., Luo, J., Yang, C. et al. Ricci-flat Graphs with Girth Four. Acta. Math. Sin.-English Ser. 37, 1679–1691 (2021). https://doi.org/10.1007/s10114-021-9546-y

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  • DOI: https://doi.org/10.1007/s10114-021-9546-y

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