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={P. Terwilliger},
  journal={Journal of Algebraic Combinatorics},
  year={2004},
  volume={19},
  pages={143-172}
}
  • P. Terwilliger
  • Published 2004
  • Mathematics
  • Journal of Algebraic Combinatorics
  • 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
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    References

    SHOWING 1-10 OF 41 REFERENCES
    2-Homogeneous bipartite distance-regular graphs
    • B. Curtin
    • Computer Science, Mathematics
    • Discret. Math.
    • 1998
    • 51
    Bipartite Distance-regular Graphs, Part I
    • 22
    The subconstituent algebra of a distance-regular graph; thin modules with endpoint one
    • 16
    • PDF
    The girth of a thin distance-regular graph
    • 26
    • PDF
    A new feasibility condition for distance-regular graphs
    • 30
    Tight Distance-regular Graphs and the Subconstituent Algebra*1
    • 25
    • Highly Influential
    Tight Distance-Regular Graphs
    • 54
    • PDF
    The Local Structure of a Bipartite Distance-regular Graph
    • B. Curtin
    • Computer Science, Mathematics
    • Eur. J. Comb.
    • 1999
    • 16
    Twice Q-polynomial distance-regular graphs are thin
    • 29
    • PDF