On Distance-Regular Graphs with Height Two
Masato Tomiyama
Kyushu University Graduate School of Mathematics Higashi-ku, Fukuoka 812 Japan
DOI: 10.1023/A:1022440414422
Abstract
Let max{ i: p di d \textonesuperior 0 } \max \left\{ {i:p_{di}^d \ne 0} \right\} . Suppose that for every 
in 
and 
in d( ), the induced subgraph on d( ) 
2( ) is a clique. Then is isomorphic to the Johnson graph J(8, 3).
in and in d( ), the induced subgraph on d( ) 2( ) is a clique. Then is isomorphic to the Johnson graph J(8, 3).Pages: 57–76
Keywords: distance-regular graph; strongly regular graph; height; clique; Johnson graph
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References
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2. E. Bannai and T. Ito, "Current researches on algebraic combinatorics," Graphs and Combin. 2 (1986), 287- 308.
3. N.L. Biggs, Algebraic Graph Theory, Cambridge University Press, Cambridge, 1974.
4. A. Boshier and K. Nomura, "A remark on the intersection arrays of distance regular graphs," J. Combin. Theory Ser. B. 44 (1988), 147-153.
5. A.E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer, Berlin-Heidelberg, 1989.
6. A.D Gardiner, C.D. Godsil, A.D. Hensel, and Gordon F. Royle, "Second neighbourhoods of strongly regular graphs," Discrete Math. 103(1992), 161-170.
7. A. Neumaier, "Characterization of a class of distance-regular graphs," J. Reine Angew. Math. 357 (1985), 182-192.
8. H. Suzuki, "Bounding the diameter of a distance regular graph by a function of kd," Graphs and Combin. 7 (1991), 363-375.
9. H. Suzuki, "Bounding the diameter of a distance regular graph by a function of kd , II," J. Algebra 169 (1994), 713-750.
10. P. Terwilliger, "The Johnson graph J(d, r) is unique if (d, r) = (2, 8)," Discrete Math. 58 (1986), 175-189.