Bounding the intersection number c2 of a distance-regular graph with classical parameters (D,b,α,β) in terms of b

초록

Let Γ be a distance-regular graph with classical parameters (D,b,α,β) and b≥1. It is known that Γ is Q-polynomial with respect to θ<inf>1</inf>, where θ<inf>1</inf>=[Formula presented]−1 is the second largest eigenvalue of Γ. And it was shown that for a distance-regular graph Γ with classical parameters (D,b,α,β), D≥5 and b≥1, if a<inf>1</inf> is large enough compared to b and Γ is thin, then the intersection number c<inf>2</inf> of Γ is bounded above by a function of b. In this paper, we obtain a similar result without the assumption that the graph Γ is thin. © 2024 Elsevier B.V.

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