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Home > Vol 19, No 3 (2004)

Brian Curtin¹ and Kazumasa Nomura²

¹Department of Mathematics University of South Florida 4202 E. Fowler Ave PHY 114 Tampa FL 33647 USA
²College of Liberal Arts and Sciences Tokyo Medical and Dental University Kohnodai, Ichikawa 272-0827 Japan

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 \mathcal{N} ( W). In this paper we study the distance-regular graphs M \mathcal{M} satisfies W M \mathcal{M} N \mathcal{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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