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Distance-regular graphs

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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)

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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