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The complete symmetric directed graph of order $v$, denoted $K_{v}^*$, is thedirected graph on $v$ vertices that contains both arcs $(x,y)$ and $(y,x)$ foreach 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 thespectrum of $D$. There are 10 non-isomorphic orientations of a $7$-cycle(heptagon). In this paper, we completely settled the spectrum problem for eachof the oriented heptagons.

Decompositions of Complete Symmetric Directed Graphs into the Oriented Heptagons