It is proved that every series-parallel digraph whose maximum vertex degree is Δ admits an upward planar drawing with at most one bend per edge such that each edge segment has one of Δ distinct slopes. The construction is worst-case optimal in terms of the number of slopes, and it gives rise to drawings with optimal angular resolution $\frac{\pi }{\mathrm{\Delta }}$. A variant of the drawing algorithm is used to show that (non-directed) reduced series-parallel graphs and flat series-parallel graphs have a (non-upward) 1-bend planar drawing with $\lceil \frac{\mathrm{\Delta }}{2}\rceil$ distinct slopes if biconnected, and with $\lceil \frac{\mathrm{\Delta }}{2}\rceil +1$ distinct slopes if connected.

中文翻译：

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SP图的一弯向上平面斜率数

事实证明，每一个最大顶点度为Δ的串并平行图都允许一个向上的平面图，每个边缘最多具有一个弯曲，使得每个边缘段都具有Δ个不同的斜率之一。就坡度的数量而言，此结构在最坏情况下是最佳的，从而产生具有最佳角度分辨率的图形$\frac{\pi }{\mathrm{\Delta }}$。绘制算法的一种变体用于显示（无向）精简系列-平行图和平面系列-平行图具有（非向上）1-弯曲平面图，其中$\lceil \frac{\mathrm{\Delta }}{2}\rceil$ 双向连接时有明显的坡度 $\lceil \frac{\mathrm{\Delta }}{2}\rceil +\mathrm{1个}$ 如果连接，则有明显的斜坡。