  It is shown that exactly 7 distance-transitive cubic graphs among the
existing 12 possess a particular ultrahomogeneous property with respect to
oriented cycles realizing the girth that allows the construction of a related
Cayley digraph with similar ultrahomogeneous properties in which those oriented
cycles appear minimally "pulled apart", or "separated" and whose description is
truly beautiful and insightful. This work is proposed as the initiation of a
study of similar ultrahomogeneous properties for distance-transitive graphs in
general with the aim of generalizing to constructions of similar related
"separator" Cayley digraphs.
