  We give a discrete Bonnet Myers type theorem for the effective diameter
assuming positive Ollivier curvature. We prove that this diameter bound is
attained if and only if the graph is a cocktail party graph, a Johnson graph, a
halved cube, a Schl\"afli graph, a Gosset graph, or a cartesian product of the
mentioned graphs with same Ollivier curvature. As a key step in the proof, we
introduce the notion of reflective graphs as graphs such that for any two
neighbors there exists a certain self-inverse automorphism mapping one neighbor
to another. We classify these graphs as arbitrary cartesian products of the
graphs mentioned before.
