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 whose girth are at least five. In this paper, we classify all of connected unweighted normalized -free graphs satisfying curvature dimension condition for minimum degree at least 2 and the case with non-normalized Laplacian without degree condition..
Keywords
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}
}