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By using Ocneanu's result on the classification of all irreducibleconnections on the Dynkin diagrams, we show that the dual principal graphs aswell as the fusion rules of bimodules arising from any Goodman-de laHarpe-Jones subfactors are obtained by a purely combinatorial method. Inparticular we obtain the dual principal graph and the fusion rule of bimodulesarising from the Goodman-de la Harpe-Jones subfactor corresponding to theDynkin diagram $E_8$. As an application, we also show some subequivalence among$A$-$D$-$E$ paragroups.

On the fusion algebras of bimodules arising from Goodman-de la Harpe-Jones subfactors