Let Γ denote a distance-biregular graph with vertex set X. Fix x∈ X and let T= T (x) denote
the Terwilliger algebra of Γ with respect to x. In this paper we consider irreducible T-modules …

Let Γ denote a bipartite graph with vertex set X and color partitions Y, Y′. For a nonnegative
integer i and a vertex x∈ X, let Γ i (x) denote the set of vertices in X that are at distance i from …

Let Γ denote a finite, simple, connected and bipartite graph. Fix a vertex x of Γ and let T= T
(x) denote the Terwilliger algebra of Γ with respect to x. Assume that x is a distance …

Let Γ denote a finite, simple and connected graph. Fix a vertex x of Γ and let T= T (x) denote
the Terwilliger algebra of Γ with respect to x. Assume that x is a distance-regularized vertex …

Terwilliger algebras are a subalgebra of a matrix algebra that are constructed from
association schemes over finite sets. In 2010, Rie Tanaka defined what it means for a …

In this thesis, we will explore the structure of Terwilliger algebras over several different types
of finite groups. We will begin by discussing what a Schur ring is, as well as providing many …

For integers n≥ 1 and m≥ 0, let D= D (n, m) denote the Doob scheme which is the direct
product of n copies of Shrikhande graph and m copies of complete graph on four vertices …

Let $\Gamma $ denote a finite, simple and connected graph. Fix a vertex $ x $ of $\Gamma $
which is not a leaf and let $ T= T (x) $ denote the Terwilliger algebra of $\Gamma $ with …

Let Γ denote an undirected, connected, regular graph with vertex set X, adjacency matrix A,
and d+ 1 distinct eigenvalues. Let A= A (Γ) denote the subalgebra of MatX (C) generated by …

Let Γ denote a bipartite distance-regular graph with diameter D≥ 4 and valency k≥ 3. Let X
denote the vertex set of Γ, and let Ai (0≤ i≤ D) denote the distance matrices of Γ. We …