Edge partitions of the complete symmetric directed graph and related designs

Abstract

We show that the edges of the complete symmetric directed graph onn vertices can be partitioned into directed cycles (or anti-directed cycles) of lengthn−1 so that any two distinct cycles have exactly one oppositely directed edge in common whenn=p e>3, wherep is a prime ande is a positive integer. When the cycles are anti-directedp must be odd. We then consider the designs which arise from these partitions and investigate their construction.