English

Graphs with nonnegative Bakry-\'Emery curvature without Quadrilateral

Combinatorics 2024-08-20 v1 Metric Geometry

Abstract

The definition of Ricci curvature on graphs in Bakry-\'Emery's sense based on curvature dimension condition was introduced by Lin and Yau [\emph{Math. Res. Lett.}, 2010]. Hua and Lin [\emph{Comm. Anal. Geom.}, 2019] classified unweighted graphs satisfying the curvature dimension condition CD(0,)CD(0,\infty) whose girth are at least five. In this paper, we classify all of connected unweighted normalized C4C_4-free graphs satisfying curvature dimension condition CD(0,)CD(0,\infty) for minimum degree at least 2 and the case with non-normalized Laplacian without degree condition..

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Cite

@article{arxiv.2408.09823,
  title  = {Graphs with nonnegative Bakry-\'Emery curvature without Quadrilateral},
  author = {Huiqiu Lin and Zhe You},
  journal= {arXiv preprint arXiv:2408.09823},
  year   = {2024}
}