Root Systems and The Johnson and Hamming Graphs

@article{Terwilliger1987RootSA,
  title={Root Systems and The Johnson and Hamming Graphs},
  author={Paul M. Terwilliger},
  journal={Eur. J. Comb.},
  year={1987},
  volume={8},
  pages={73-102}
}
In [27] we show that any distance-regular graph Г containing a cycle {ν 0 , ν 1 , ν 2 , ν 3 , ν 0 } with δ(ν 0 , ν 2 ) = δ(ν 1 , ν 3 ) = 2 was finite, with diameter d , valency k and intersection numbers a 1 , c d satisfying d ⩽ k + c d a i + 2 with equality holding if and only if (1) c i − c i − 1 + b i − 1 − b i − a 1 − 2 = 0 , ( 1 ⩽ i ⩽ d ) In this graph we give a simplified proof of this fact, and then classify the graphs where the diameter bound is attained. Not assuming the existence of… CONTINUE READING