Abstract
Ph.D.
In this thesis, the ranks of many types of regular and strongly regular graphs are
determined. Also determined are ranks of regular graphs under unary operations: the line
graph, the complement, the subdivision graph, the connected cycle, the complete
subdivision graph, and the total graph. The binary operations considered are the
Cartesian product and the complete product. The ranks of the Cartesian product of
regular graphs have been investigated previously in [BBD1]; here, we summarise and
extend those results to include more regular graphs. We also examine a special nonregular graph, the path. Ranks of paths and products of graphs involving paths are
presented as well