Decompositions of complete symmetric directed graphs into the oriented heptagons

Abstract

The complete symmetric directed graph of order v , denoted by K∗ v , is the directed graph on v vertices that contains both arcs (x, y) and (y, x) for each pair of distinct vertices x and y . For a given directed graph D, the set of all v for which K∗ v admits a D-decomposition is called the spectrum of D-decomposition. There are 10 nonisomorphic orientations of a 7-cycle (heptagon). In this paper, we completely settled the spectrum problem for each of the oriented heptagons.