How to draw combinatorial maps?

Abstract

In this article we consider the combinatorial map (rendered by permutations) approach to graphs on surfaces and how between both could be establish some terminological uniformity in favor of combinatorial maps in the way rotations were set as fundamental structural elements, and other necessary notions were derived from them. We call this the rotational prevalence with respect to how to build a graph drawing environment. We deal here with simple operations of how to draw combinatorial maps and partial maps. One of our aims would be to advocate a wider use of combinatorial maps in the graph drawing applications. Besides, we advocate to use corners of halfedges where upon permutations act in place of halfedges.