论文标题
完全对称的定向图的分解到定向的七个
Decompositions of Complete Symmetric Directed Graphs into the Oriented Heptagons
论文作者
论文摘要
订单$ v $的完整对称有向图，表示为$ k_ {v}^*$，是$ v $顶点上的指向图，其中包含弧线$（x，y）$和$（y，x）$（y，x）$（y，x）$，每对不同的顶点$ x $和y $。对于给定的有向图，$ d $，$ k_ {v}^*$的所有$ v $的集合被称为$ d $ dectrum $ d $。 $ 7 $ cycle（Heptagon）有10个非同态取向。在本文中，我们完全解决了每个定向的七琴的频谱问题。
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.
