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

For a finite connected simple graph, the Terwilliger algebra is a matrix algebra generated by the adjacency matrix and idempotents corresponding to the distance partition with respect to a fixed vertex. We will consider algebras defined by two other partitions and the centralizer algebra of the stabilizer of the fixed vertex in the automorphism group of the graph. We will give some methods to compute such algebras and examples for various graphs. (c) 2023 Elsevier B.V. All rights reserved.