Simple drawings are drawings of graphs in which any two edges intersect at most once (either at a common endpoint or a proper crossing), and no edge intersects itself. We analyze several characteristics of simple drawings of complete multipartite graphs: which pairs of edges cross, in which order they cross, and the cyclic order around vertices and crossings, respectively. We consider all possible combinations of how two drawings can share some characteristics and determine which other characteristics they imply and which they do not imply. Our main results are that for simple drawings of complete multipartite graphs, the orders in which edges cross determine all other considered characteristics. Further, if all partition classes have at least three vertices, then the pairs of edges that cross determine the rotation system and the rotation around the crossings determine the extended rotation system. We also show that most other implications -- including the ones that hold for complete graphs -- do not hold for complete multipartite graphs. Using this analysis, we establish which types of isomorphisms are meaningful for simple drawings of complete multipartite graphs.

翻译：简单绘制是指图中任意两条边至多相交一次（要么在公共端点处相交，要么恰好横穿交叉），且无边自我交叉。我们分析了完全多部图简单绘制的几个特征：哪些边对交叉、交叉的次序、以及顶点和交叉点周围的循环顺序。我们考虑了两种绘制共享某些特征的所有可能组合，并确定了它们暗示或不暗示的其他特征。我们的主要结果是：对于完全多部图的简单绘制，边的交叉顺序决定了所有其他被考虑的特征。此外，如果所有划分类别至少包含三个顶点，那么交叉的边对决定了旋转系统，而交叉点周围的旋转决定了扩展旋转系统。我们还表明，大多数其他蕴含关系——包括完全图中所成立的——对于完全多部图并不成立。基于这一分析，我们确定了哪些类型的同构对完全多部图的简单绘制具有意义。