Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing the planarization process by algebraic methods, without making any geometric constructions on the plane. Constructing a rotation of graph vertices solves two most important problems of graph theory simultaneously: the problem of testing a graph for planarity and the problem of constructing a topological drawing of a planar graph. It is shown that the problem of constructing a drawing of a non-planar graph can be reduced to the problem of constructing a drawing of a planar graph, taking into account the introduction of additional vertices characterizing the intersection of edges. Naturally, the development of such a mathematical structure will make it possible to solve the following important problems of graph theory: testing the planarity of a graph, identifying the largest planar subgraph of a graph, determining the thickness of a graph, obtaining a graph with a minimum number of intersections, etc.

翻译：现代图论方法在描述图时通常只考虑同构关系，这使得为平面上的图绘制可视化创建数学模型变得困难。图的平面部分的拓扑绘制允许通过代数方法表示平面化过程，而无需在平面上进行任何几何构造。构建图顶点的旋转同时解决了图论中两个最重要的问题：图的平面性测试问题以及平面图的拓扑绘制构造问题。研究表明，非平面图的绘制问题可以简化为平面图的绘制问题，只需考虑引入表征边相交的额外顶点。自然地，这种数学结构的发展将使得解决以下图论重要问题成为可能：图的平面性测试、识别图的最大平面子图、确定图的厚度、获得具有最少交叉次数的图等。