An Inequality Involving the Local Eigenvalues of a Distance-Regular Graph

@article{Terwilliger2004AnII,
  title={An Inequality Involving the Local Eigenvalues of a Distance-Regular Graph},
  author={Paul Terwilliger},
  journal={Journal of Algebraic Combinatorics},
  year={2004},
  volume={19},
  pages={143-172}
}
AbstractLet Γ denote a distance-regular graph with diameter D ≥ 3, valency k, and intersection numbers ai, bi, ci. Let X denote the vertex set of Γ and fix x ∈ X. Let Δ denote the vertex-subgraph of Γ induced on the set of vertices in X adjacent X. Observe Δ has k vertices and is regular with valency a1. Let η1 ≥ η2 ≥ ··· ≥ ηk denote the eigenvalues of Δ and observe η1 = a1. Let Φ denote the set of distinct scalars among η2, η3, ..., ηk. For η ∈ Φ let multη denote the number of times η appears… CONTINUE READING