  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.
