The lexicographic product Γ′=Γ from Γ to C*r is constructed and the equivalent conditions for it being a weakly distance-regular digraphs is given.

In this paper , we discuss the constructions of lexicographic product and directed product from weakly distance-regular digraphs to undirected graphs, and of lexicographic product from a digraph to a digraph.

In this paper we obtain techniques for computing the characteristic polynomials of ordinary digraphs graph theory and determining relations of characteristic polynomials about weakly regular digraph and its complement.

On distance-regular graphs with height one and three;

Inequalities of cosine sequences for distance-regular graphs of type E_1 ~oE_d;

Using intersection diagram,investigated the distance-regular graph with diameter d≥3 and hight 2,obtained some new properties of this type of graph.

By using the eigenvalue techniques and properties of intersection numbers,it is obtained that the distance regular graphs with the following intersection arrays are nonexistence.

By mean of intersection diagrams,properties of distance-regular graphs and the known conclusions of distance-regular graphs in this thesis,we discuss intersection numbers of distance-regular graphs.

In this paper, we characterize the distance-regular graphs of type E1(?)Ed with a generalized feasible cosine sequence, and obtain the intersection numbers of these graphs.