On m-partite oriented semiregular representations of finite groups generated by two elements

In this paper we extend the notion of oriented regular representations in the context of m -partite oriented digraphs with an integer m >= 2. A group G is said to admit an m-partite oriented semiregular representation ( m -POSR for short) if there exists an m -partite oriented digraph such that its automorphism group is isomorphic to G and acts semiregularly on vertices with every part of the digraph as an orbit. In this paper, we proved that G admits an m -POSR of valency two except for several cases when G is a finite group generated by at most two elements and m >= 2 is an integer. (c) 2024 Published by Elsevier B.V.