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A note on non-regular Bonnet-Myers Sharp Graphs
Published 7 May 2024 in math.CO | (2405.04703v1)
Abstract: Self-centred regular graphs which are Ollivier-Ricci Bonnet-Myers sharp have been completely classified. When the conditions of self-centeredness and regularity are removed it is an open problem on what the classification is. We present a complete classification of Bonnet-Myers sharp graphs with a diameter 2 and show that there exists Bonnet-Myers sharp graphs of diameter 3, 4 and 6 that belong to a family of graphs called symmetrical antitees.
- David Cushing and Supanat Kamtue and Shiping Liu and Florentin Muench and Norbert Peyerimhoff, Rigidity of the Bonnet-Myers inequality for graphs with respect to Ollivier Ricci curvature. Advances in mathematics 360 (2020).
- David Cushing and Shiping Liu and Florentin Münch and Norbert Peyerimhofff, Curvature calculations for antitrees. Analysis and geometry on graphs and manifolds. (2018).
- Supanat Kamtue, Bonnet-Myers sharp graphs of diameter three. https://arxiv.org/abs/2005.06704 (2020).
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