This is a survey of distance-regular graphs. We present an introduction to distance-regular
graphs for the reader who is unfamiliar with the subject, and then give an overview of some …

Let Γ= Γ (n, m) denote the Doob graph formed by the Cartesian product of the nth Cartesian
power of the Shrikhande graph and the mth Cartesian power of the complete graph on four …

There is a concept in linear algebra called a tridiagonal pair. The concept was motivated by
the theory of $ Q $-polynomial distance-regular graphs. We give a tutorial introduction to …

Let F be an algebraically closed field with char (F)= 0. The special linear algebra sl 2 is the F-
Lie algebra with Chevalley basis {e, h, f}. Since the special orthogonal algebra so 4 is …

Abstract In 2007, B. Hartwig and Terwilliger found a presentation for the three-point sl 2 loop
algebra in terms of generators and relations. To obtain this presentation, they defined a Lie …

For fixed integers n ≥ 1 n≥ 1 and m ≥ 0 m≥ 0, we consider the Doob graph D= D (n, m)
D= D (n, m) formed by taking direct product of n copies of Shrikhande graph and m copies of …

The tetrahedron algebra $\boxtimes $ is an infinite-dimensional Lie algebra defined by
generators $\{x_ {ij}\mid i, j\in\{0, 1, 2, 3\}, i\neq j\} $ and some relations, including the Dolan …

Let F denote an algebraically closed field with characteristic 0, and let q denote a nonzero
scalar in F that is not a root of unity. Let Z 4 denote the cyclic group of order 4. Let□ q denote …

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 …

We introduce a linear algebraic object called a bidiagonal triad. A bidiagonal triad consists
of three diagonalizable linear transformations on a finite-dimensional vector space which …