This is the third, and last, of a series of papers dealing with oriented regular representations.
Here we complete the classification of finite groups that admit an oriented regular …

A Frobenius group is a transitive permutation group that is not regular and such that only the
identity fixes more than one point. A graphical Frobenius representation (GFR) of a …

A Frobenius group is a transitive permutation group that is not regular and such that only the
identity fixes more than one point. A digraphical, respectively graphical, Frobenius …

Let $ R $ be a group and let $ S $ be a subset of $ R $. The Haar graph $\mathrm {Haar}(R,
S) $ of $ R $ with connection set $ S $ is the graph having vertex set $ R\times\{-1, 1\} …

We give a complete answer to the GFR conjecture, proposed by Conder, Doyle, Tucker and
Watkins:“All but finitely many Frobenius groups F= N⋊ H with a given complement H have a …

In this paper, we investigate finite groups admitting an oriented regular representation and
we give a partial answer to a 1980 question of Lazslo Babai:“Which [finite] groups admit an …

Let G be a finite group and X a (di) graph. If there exists a semiregular subgroup G¯ of the
automorphism group Aut (X) isomorphic to G with n orbits on V (X) then the (di) graph X is …

Let G be a finite non-abelian simple group and let Γ be a connected tetravalent 2-arc-
transitive G-regular graph. In 2004, Fang, Li, and Xu proved that either G is normal in the full …

In this paper we extend the classical notion of digraphical and graphical regular
representation of a group and we classify, by means of an explicit description, the finite …

We show that every finitely generated group G with an element of order at least\bigl (5\,
rank\,(G)\bigr)^ 12 (5 rank (G)) 12 admits a locally finite directed Cayley graph with …