Abstract
Let Γ denote a distance-biregular graph with vertex set X. Fix x∈X and let T=T(x) denote the Terwilliger algebra of Γ with respect to x. In this paper we consider irreducible T-modules with endpoint 1. We show that there are no such modules if and only if Γ is the complete bipartite graph K1,n(n≥1) and x is a vertex of Γ with valency 1. If the valency of x is at least 2 then we show that up to isomorphism there is a unique irreducible T-module of endpoint 1, and this module is thin.
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