I study a distance-regular graph by its subgraphs, especially for those distance-regular subgraphs. I study the finite geometry constructed from these subgraphs. I study distance-regular with more algebraic assumptions (e.g. the Q-polynomial property), and more combinatorial assumptions (e.g. Assume the graph contains no triangles, no kites, no parallelogram or even assumes it is a near polygon)
The following references including all the technique I need in the study of distance-regular graphs:
1. E. Bannai and T. Ito, Algebraic Combinatorics: Association Schemes, Lecture 58, Benjamin-Cummings, Menlo Park, 1984.
2. A. E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer Verlag, New York, 1989.
3. P. Terwilliger, The subconstituent algebra of an association scheme I, Alg., Combin. 1(4):363-388, 1992.
4. P. Terwilliger, A new inequality for distance-regular graphs, Discrete Math., 137:319-332, 1995.
5. P. Terwilliger, Kite-free distance-regular graphs, European Journal of Comb., 16:201-207, 1995.