On the Terwilliger algebra of distance-biregular graphs

DOI10.1016/j.laa.2020.03.016zbMath1448.05099OpenAlexW3010708887MaRDI QIDQ2174090

Štefko Miklavič, Blas Fernández

Publication date: 17 April 2020

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2020.03.016

zbMATH Keywords

Terwilliger algebrairreducible moduledistance biregular graph

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items (5)

On the trivial \(T\)-module of a graph ⋮ On standard bases of irreducible modules of Terwilliger algebras of Doob schemes ⋮ On bipartite graphs with exactly one irreducible \(T\)-module with endpoint 1, which is thin ⋮ Certain graphs with exactly one irreducible \(T\)-module with endpoint 1, which is thin ⋮ On (almost) \(2\)-\(Y\)-homogeneous distance-biregular graphs

Cites Work

• The spectral excess theorem for distance-biregular graphs.
• Pseudo-distance-regularized graphs are distance-regular or distance-biregular
• On Lee association schemes over \(\mathbb{Z}_4\) and their Terwilliger algebra
• On bipartite distance-regular graphs with exactly two irreducible T-modules with endpoint two
• The subconstituent algebra of an association scheme. I
• On the Terwilliger algebra of bipartite distance-regular graphs with \(\Delta_2 = 0\) and \(c_2 = 2\)
• Terwilliger algebras of wreath products of association schemes
• Distance-biregular graphs with 2-valent vertices and distance regular line graphs
• Locally pseudo-distance-regular graphs
• Distance biregular bipartite graphs
• An \(A\)-invariant subspace for bipartite distance-regular graphs with exactly two irreducible \(T\)-modules with endpoint 2, both thin
• On bipartite \(Q\)-polynomial distance-regular graphs with diameter 9, 10, or 11
• 1-homogeneous, pseudo-1-homogeneous, and 1-thin distance-regular graphs
• The Terwilliger algebra of a distance-regular graph that supports a spin model
• The Terwilliger algebra of the incidence graph of the Hamming graph
• Distance-regularised graphs are distance-regular or distance-biregular
• The quantum adjacency algebra and subconstituent algebra of a graph
• On bipartite distance-regular graphs with exactly one non-thin \(T\)-module with endpoint two
• Intersection diagrams of distance-biregular graphs
• On pseudo-distance-regularity
• On the algebraic theory of pseudo-distance-regularity around a set
• On the Terwilliger algebra of bipartite distance-regular graphs with \(\Delta_{2}=0\) and \(c_{2}=1\)

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