Homogeneity of a Distance-Regular Graph Which Supports a Spin Model
نویسندگان
چکیده
A spin model is a square matrix that encodes the basic data for a statistical mechanical construction of link invariants due to V.F.R. Jones. Every spin model W is contained in a canonical Bose-Mesner algebra N (W ). In this paper we study the distance-regular graphs whose Bose-Mesner algebra M satisfies W ∈ M ⊆ N (W ). Suppose W has at least three distinct entries. We show that is 1-homogeneous and that the first and the last subconstituents of are strongly regular and distance-regular, respectively.
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