The definition of Ricci curvature on graphs in Bakry-\'Emery's sense based on curvature dimension condition was introduced by Lin and Yau [Math. Res. Lett., 2010]. Hua and Lin [Comm. Anal. Geom., 2019] classified unweighted graphs satisfying the curvature dimension condition CD(0,∞) whose girth are at least five. In this paper, we classify all of connected unweighted normalized C₄-free graphs satisfying curvature dimension condition CD(0,∞) for minimum degree at least 2 and the case with non-normalized Laplacian without degree condition..
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Lin et al. (2024) studied this question.
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