Near-Rotational Directed Triple Systems

A directed triple system of order \(v\), denoted \(DT S(v)\), is said to be \(k\)-near-rotational if it admits an automorphism consisting of \(3\) fixed points and \(k\) cycles of length \(\frac{v-3}{3}\). In this paper, we give necessary and sufficient conditions for the existence of \(k\)-near-rotational \(DT S(v)\)s.