A graph $G$ is a non-separating planar if there drawing $D$ of on the plane such that (1) no two edges cross each other in and (2) for any cycle $C$ $D$, vertices not are same side $D$.
 Non-separating graphs closed under taking minors subclass superclass outerplanar graphs.
 In this paper, we show only it does contain $K_1 \cup K_4$ or K_{2,3}$ $K_{1,1,3}$ as minor.
 Furthermore...

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