Shilla distance-regular graphs

@article{Koolen2010ShillaDG,
  title={Shilla distance-regular graphs},
  author={Jacobus H. Koolen and Jongyook Park},
  journal={Eur. J. Comb.},
  year={2010},
  volume={31},
  pages={2064-2073}
}
A Shilla distance-regular graph Γ (say with valency k) is a distance-regular graph with diameter 3 such that its second largest eigenvalue equals to a3. We will show that a3 divides k for a Shilla distance-regular graph Γ, and for Γ we define b = b(Γ) := k a3 . In this paper we will show that there are finitely many Shilla distance-regular graphs Γ with fixed b(Γ) ≥ 2. Also, we will classify Shilla distance-regular graphs with b(Γ) = 2 and b(Γ) = 3. Furthermore, we will give a new existence… CONTINUE READING

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Coolsaet , A distance - regular graph with intersection array { 21 , 16 , 8 ; 1 , 4 , 14 } does not exist

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