Rectangle-Visibility Representation of Products of Graphs

Thesis (M.A.) from the year 2017 in the subject Mathematics - Applied Mathematics, grade: 80.0, Kwame Nkrumah University of Science and Technology (AIMS-GH), course: M.Sc Mathematical Sciences, language: English, abstract: Visibility representation of a graph is a way of assigning the vertices of a graph to objects in a plane and the edges of the graph representing the positioning of the objects in such a way that they see one another. In this work, we consider representations of products of some classes of graphs as rectangle-visibility graphs (RVGs), i.e, graphs whose vertices are rectangles in the plane and edges are horizontal or vertical visibility. We focus on three types of graph products namely: cartesian, direct and strong products. We also investigate representations of products of some classes of graphs such as path, cycle with path, star with path and complete graphs that are RVGs. Furthermore, we discuss why some complete graphs are not RVGs. The results obtained are established by constructive proofs and yield linear-time layout.