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For a finite connected simple graph, the Terwilliger algebra is a matrixalgebra generated by the adjacency matrix and idempotents corresponding to thedistance partition with respect to a fixed vertex. We will consider algebrasdefined by two other partitions and the centralizer algebra of the stabilizerof the fixed vertex in the automorphism group of the graph. We will give somemethods to compute such algebras and examples for various graphs.

Terwilliger algebras and some related algebras defined by finite connected simple graphs