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arXiv · 1807.07253

Ricci-flat graphs with girth four

Weihua He·Jun Luo·Chao Yang·Wei Yuan
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Abstract

Lin-Lu-Yau introduced an interesting notion of Ricci curvature for graphs and obtained a complete characterization for all Ricci-flat graphs with girth at least five [1]. In this paper, we propose a concrete approach to construct an infinite family of distinct Ricci-flat graphs of girth four with edge-disjoint 4-cycles and completely characterize all Ricci-flat graphs of girth four with vertex-disjoint 4-cycles.

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Weihua He, Jun Luo, Chao Yang, Wei Yuan. 2018-07-19. Ricci-flat graphs with girth four. https://arxiv.org/abs/1807.07253

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