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Home > Vol 7, No 2 (1998)

Masato Tomiyama

Let d \geqslant 3 d \geqslant 3 and height h = 2 h = 2 , where h = max{ i: p _{d, i} ^d \textonesuperior  0} h = max\{ i:p_{d,i}^d \ne 0\} . Suppose that for every G _d ( a) Γ_d (α) , the induced subgraph on G _d ( a) Ç G ₂ ( b) Γ_d (α) \cap Γ_2 (β) is isomorphic to a complete multipartite graph K _{t \times 2} K_{t \times 2} with t \geqslant 2 t \geqslant 2 . Then d = 4 d = 4 and J(10,4) \begin{gathered} J(10,4) \hfill \\ \hfill \\ \end{gathered} .

1. E. Bannai and T. Ito, Algebraic Combinatorics I, Benjamin-Cummings, California, 1984.
2. N. L. Biggs, Algebraic Graph Theory, Cambridge University Press, Cambridge, 1974.
3. A. E. Brouwer, A. M. Cohen and A. Neumaier, Distance-Regular Graphs, Springer, Berlin-Heidelberg, 1989 TOMIYAMA
4. A. Neumaier, “Characterization of a class of distance regular graphs,” J. Reine Angew. Math 357 (1985), 182-192.
5. K. Nomura, “An application of intersection diagrams of high rank,” Discrete Math. 127 (1994), 259-264.
6. H. Suzuki, “Bounding the diameter of a distance regular graph by a function of kd,” Graphs and Combin. 7 (1991), 363-375.
7. H. Suzuki, “Bounding the diameter of a distance regular graph by a function of kd, II,” J. Algebra 169 (1994), 713-750.
8. H. Suzuki, “On distance-i-graphs of distance-regular graphs,” Kyushu J. Math. 48 (1994), 379-408.
9. H. Suzuki, “On distance regular graphs with be = 1,” SUT J. Math. 29 (1993), 1-14.
10. H. Suzuki, “A note on association schemes with two P-polynomial structures of type III,” J. Combin. Theory Ser. A 74 (1996), 158-168.
11. D. H. Smith, “On bipartite tetravalent graphs,” Discrete Math. 10 (1974), 167-172.
12. P. Terwilliger, “The Johnson graph J (d, r) is unique if (d, r) = (2, 8),” Discrete Math. 58 (1986), 175-189.
13. M. Tomiyama, “On distance-regular graphs with height two,” J. Alg. Combin. 5 (1996), 57-76.