This work concerns itself with Topological Graph Theory. This includes vector representations of graphs, regular connected graphs which are locally paths, and graphical designs. Also edge decompositions of a complete graph on n vertices represented by a set of n vectors from a suitable vector space will be studied. Finally more algebraic problems including combinatorial aspects of determinants and Hamiltonian groups will be investigated. Topological Graph Theory uses the deep tools of topology to study graphs. Graphs themselves are an increasingly important tool in many areas including computer science and the social sciences. This research will concentrate on graphs and their applications.
