A note on non-regular Bonnet-Myers Sharp Graphs

TL;DR

This paper classifies Bonnet-Myers sharp graphs with diameter 2 and explores the existence of such graphs with larger diameters, introducing the family of symmetrical antitees.

Contribution

It provides a complete classification of diameter-2 Bonnet-Myers sharp graphs and identifies new examples with larger diameters within the symmetrical antitees family.

Findings

Complete classification of diameter-2 Bonnet-Myers sharp graphs

Existence of Bonnet-Myers sharp graphs with diameters 3, 4, and 6

Introduction of symmetrical antitees as a new graph family

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.