Distance-regular graphs

Distance-regular graphs were introduced by Biggs around 1970 as a combinatorial generalization of distance-transitive graphs. They became popular after Delsarte studied codes in these graphs. Many objects are closely related to distance-regular graphs, for example, coding theory, design theory, finite geometry, and group theory. Click here for a diagram of these relations

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.

updated since 12/15/03