On Distance-Regular Graphs With Fixed Hight

In this thesis, we consider the distance-regular graphs with diameter d ≥ 3 and hight h = 1,2, and3, where h= max{i|Pddi ≠ 0}. In the first place, we study the intersection diagram of rank I, and obtain some new properties of intersection numbers.Secondly, using intersection diagram, we study the distance-regular graph with diameter d > 3 and hight h = 1. We show that if bd-1 = 1 and cd≠ a2d, then the diameter d of the graph is bounded by a function depending only on a1. We also obtain some new properties of intersection numbers of the graph.Finally, using intersection diagram, we study the distance-regular graphs with diameter d ≥ 3 and hight h = 2, or 3. We give some new properties of intersection numbers of these graphs.