Rotational circulant graphs

Abstract

A Frobenius group is a transitive permutation group which is not regular but only the identity element can fix two points. Such a group can be expressed as the semidirect product G=K⋊H of a nilpotent normal subgroup K and another group H fixing a point. A first-kind G-Frobenius graph is a connected Cayley graph on K with connection set an H-orbit aH on K that generates K, where H has an even order or a is an involution. It is known that the first-kind Frobenius graphs admit attractive routing and gossiping algorithms. A complete rotation in a Cayley graph on a group G with connection set S is an automorphism of G fixing S setwise and permuting the elements of S cyclically. It is known that i..