Cayley graphs of the group ℤ4 that are limits of minimal vertex-primitive graphs of type HA

In the joint paper by Giudici, Li, Praeger, Seress, and Trofimov, it is proved that any graph that is a limit of vertex-primitive graphs of type HA is isomorphic to a Cayley graph of the group ℤ d . Earlier, the author proved that for d ≤ 3 the number of pairwise nonisomorphic Cayley graphs of the group ℤ d , which are limits of minimal vertex-primitive graphs of type HA, is finite (and obtained their explicit description). The present paper includes the construction of a countable family of such graphs for the case d = 4; moreover, up to isomorphism there are only finitely many Cayley graphs of such a type outside this family. © 2007 Pleiades Publishing, Ltd.