# Bipartite distance-regular graphs with exactly two irreducible $T$-modules with endpoint 2, both thin

### Štefko Miklavič University of Primorska

#### Mark MacLean Seattle University

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Minisymposium: ASSOCIATION SCHEMES

Content: Let $\Gamma$ denote a bipartite distance-regular graph with diameter $D \ge 4$ and valency $k \ge 3$. Let $X$ denote the vertex set of $\Gamma$. Fix $x \in X$ and let $T=T(x)$ denote the corresponding Terwilliger algebra of $\Gamma$. In this talk we consider the situation where, up to isomorphism, $\Gamma$ has exactly two irreducible $T$-modules with endpoint $2$, and they are both thin. Our main result is a combinatorial characterization of this situation.

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