The Arc-Connectivity of 3-Regular Digraphs with Two Orbits

Abstract

Let [Formula: see text] be a simple strongly connected digraph and let Aut[Formula: see text] be an automorphism of [Formula: see text]. For [Formula: see text], the set [Formula: see text] is called an orbit of Aut[Formula: see text]. In this paper, first, we show that if [Formula: see text] is a 2-regular strongly connected digraph with two orbits then [Formula: see text], if [Formula: see text] is a [Formula: see text]-regular strongly connected digraph with two orbits and [Formula: see text] [Formula: see text], then [Formula: see text]. Second, we prove that if [Formula: see text], then [Formula: see text]. Last, we characterize the arc atoms of 3-regular strongly connected digraphs with two orbits and [Formula: see text].