Embeddings of Harary Graphs in Orientable Surfaces
Christopher Allen Smith · DigitalCommons (California Polytechnic State University) · 2019
The purpose of this thesis is to study embeddings of Harary graphs in orientable surfaces. In particular, our goal is to provide a complete description of one method of constructing a maximal embedding in an orientable surface for any Harary graph. Rotation systems, which describe the ordering of edges around the vertices of a graph, can be used to represent graph embeddings in orientable surfaces. Together with the Boundary Walk Algorithm, this representation provides a method of constructing a corresponding graph embedding. By switching adjacent edges in a rotation system, we can control the genus of the constructed embedding surface. We will explore how certain series of adjacent edge switches may be used to take standard rotation systems (which will be defined) to rotation systems corresponding to maximal embeddings of Harary graphs.