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

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