Taut distance-regular graphs and the subconstituent algebra

Details Taut distance-regular graphs and the subconstituent algebra Taut distance-regular graphs and the subconstituent algebra

2005-08-21

arxiv.org/abs/math/0508399v1

Mathematics

Combinatorics

29 pages

Scientific paper

We consider a bipartite distance-regular graph $G$ with diameter $D$ at least 4 and valency $k$ at least 3. We obtain upper and lower bounds for the local eigenvalues of $G$ in terms of the intersection numbers of $G$ and the eigenvalues of $G$. Fix a vertex of $G$ and let $T$ denote the corresponding subconstituent algebra. We give a detailed description of those thin irreducible $T$-modules that have endpoint 2 and dimension $D-3$. In an earlier paper the first author defined what it means for $G$ to be taut. We obtain three characterizations of the taut condition, each of which involves the local eigenvalues or the thin irreducible $T$-modules mentioned above.

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