Separating rank 3 graphs

John Bamberg, Michael Giudici, Jesse Lansdown, Gordon F. Royle

Published 2022-11-04Version 1

We classify, up to some notoriously hard cases, the rank 3 graphs which fail to meet either the Delsarte or the Hoffman bound. As a consequence, we resolve the question of separation for the corresponding rank 3 primitive groups and give new examples of synchronising, but not $\mathbb{Q}\mathrm{I}$, groups of affine type.