On distance-regular graphs with ki=kj, II

The thesis is an exposition of the article of A. Hiraki, H. Suzuki and M. Wajima entitled On Distance-Regular Graphs with ki = kj, II which is an improvement of H. Suzuki\u27s paper. Major results such as the alternative proof of Terwilliger\u27s inequality for bipartite distance-regular graphs and the refinement of Ivanov\u27s diameter bound are worked out in a more comprehensible mathematical language. Moreover, assume that T is a distance-regular graph of diameter d and i-th valency ki, where ki is the number of points at distance i from a vertex u in T. In addition, T satisfies ki = kj with i + j less than or equal to d. This study establishes the detailed proofs that T is a polygon (K=2) or an antipodal 2-cover (kd=1) by pressing definitions, lemmas and propositions with their corresponding examples and proofs