Almost 2-homogeneous bipartite distance-regular graphs

DOI10.1006/eujc.2000.0399zbMath1002.05069OpenAlexW2022866238MaRDI QIDQ1587907

Curtin, Brian

Publication date: 3 December 2000

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/eujc.2000.0399

zbMATH Keywords

Terwilliger algebradiameteradjacency matrixsubconstituentthin irreducible \(T\)-module

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Distance in graphs (05C12)

Related Items (21)

On bipartite distance-regular graphs with exactly one non-thin \(T\)-module with endpoint two ⋮ 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 ⋮ The subconstituent algebra of a strongly regular graph ⋮ Bipartite distance-regular graphs: the \(Q\)-polynomial property and pseudo primitive idempotents ⋮ On the Terwilliger algebra of certain family of bipartite distance-regular graphs with Δ_2 = 0 ⋮ On bipartite \(Q\)-polynomial distance-regular graphs with \(c_2 \leqslant 2\) ⋮ Pseudo primitive idempotents and almost 2-homogeneous bipartite distance-regular graphs ⋮ On bipartite distance-regular graphs with exactly two irreducible T-modules with endpoint two ⋮ The subconstituent algebra of a bipartite distance-regular graph; thin modules with endpoint two ⋮ On bipartite \(Q\)-polynomial distance-regular graphs with diameter 9, 10, or 11 ⋮ Triangle- and pentagon-free distance-regular graphs with an eigenvalue multiplicity equal to the valency ⋮ Algebraic characterizations of graph regularity conditions ⋮ 1-homogeneous, pseudo-1-homogeneous, and 1-thin distance-regular graphs ⋮ On the Terwilliger algebra of bipartite distance-regular graphs with \(\Delta_2 = 0\) and \(c_2 = 2\) ⋮ On the Terwilliger algebra of bipartite distance-regular graphs with \(\Delta_{2}=0\) and \(c_{2}=1\) ⋮ Almost 2-homogeneous graphs and completely regular quadrangles ⋮ Bipartite distance-regular graphs and taut pairs of pseudo primitive idempotents ⋮ An inequality involving the local eigenvalues of a distance-regular graph ⋮ The subconstituent algebra of a distance-regular graph; thin modules with endpoint one ⋮ Tight distance-regular graphs and the subconstituent algebra

Cites Work

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• The girth of a thin distance-regular graph
• The subconstituent algebra of an association scheme. I
• Strongly regular graphs having strongly regular subconstituents
• Strongly regular graphs and spin models for the Kauffman polynomial
• Classification of a class of distance-regular graphs via completely regular codes
• The Terwilliger algebras of bipartite \(P\)- and \(Q\)-polynomial schemes
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• Spin models for link polynomials, strongly regular graphs and Jaeger's Higman-Sims model
• Homogeneous graphs and regular near polygons
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• Orthogonal Polynomials, Duality and Association Schemes
• On the uniqueness of a certain thin near octagon (or partial 2-geometry, or parallelism) derived from the binary Golay code
• Distance-regular graphs related to the quantum enveloping algebra of \(sl(2)\)

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