  The complete symmetric directed graph of order $v$, denoted $K_{v}^*$, 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 $D$. There are 10 non-isomorphic orientations of a $7$-cycle
(heptagon). In this paper, we completely settled the spectrum problem for each
of the oriented heptagons.

Combinatorics