Near-Rotational Directed Triple Systems

Abstract

A directed triple system of order $v$, denoted $DTS(v)$, 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 $DTS(v)$s.