Ranks Of Regular Graphs Under Certain Binary Operations

The research of ranks of graph has some theoretical significance, and some practical application values. It has something to do with a graph's diameter, clique, radius and the control number. Through the research, we can deepen the understanding of a graph's structure and property. Moreover, We can find many direct utilization on the ranks of a graph in physics, chemistry and operations research.In chapter 2, We discuss the ranks of many classes of some strongly regular graph.In chapter 3, we investigate the operating problem of some regular graph and strongly regular graphs under certain binary graph product: Mainly including the structures and ranks of Cartesian product, complete product, categorical product lexicographic product and strong product. And we have obtained a series of results and further developed the conclusion drawn by C.R.Garner, G.J.Davis and G.S.Domke's.