The girth of a thin distance-regular graph

DOI10.1007/BF01202234zbMath0878.05084OpenAlexW2078129287MaRDI QIDQ675886

Benjamin V. C. Collins

Publication date: 11 March 1997

Published in: Graphs and Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01202234

zbMATH Keywords

Terwilliger algebradistance-regular graphdiametergirthregular generalized quadranglethin graph

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Generalized quadrangles and generalized polygons in finite geometry (51E12) Distance in graphs (05C12)

Related Items

The geometric girth of a distance-regular graph having certain thin irreducible modules for the Terwilliger algebra ⋮ On bounding the diameter of a distance-regular graph ⋮ The subconstituent algebra of a strongly regular graph ⋮ The subconstituent algebra of a bipartite distance-regular graph; thin modules with endpoint two ⋮ The Terwilliger algebra of a distance-regular graph of negative type ⋮ A generalization of the Terwilliger algebra ⋮ The Terwilliger algebra of the hypercube ⋮ Algebraic characterizations of graph regularity conditions ⋮ Two linear transformations each tridiagonal with respect to an eigenbasis of the other ⋮ The Terwilliger algebra of an almost-bipartite \(P\)- and \(Q\)-polynomial association scheme ⋮ \(Q\)-polynomial distance-regular graphs with \(a_1=0\) and \(a_2\neq 0\) ⋮ An inequality involving the local eigenvalues of a distance-regular graph ⋮ Distance-regular graphs which support a spin model are thin ⋮ The Terwilliger algebras of bipartite \(P\)- and \(Q\)-polynomial schemes ⋮ Almost 2-homogeneous bipartite distance-regular graphs ⋮ The subconstituent algebra of a distance-regular graph; thin modules with endpoint one ⋮ The generalized Terwilliger algebra and its finite-dimensional modules when \(d=2\) ⋮ Tight distance-regular graphs and the subconstituent algebra

Cites Work

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• The irreducible modules of the Terwilliger algebras of Doob schemes
• The subconstituent algebra of an association scheme. I
• The subconstituent algebra of an association scheme. III
• The subconstituent algebra of an association scheme. II
• Distance-transitive graphs and generalized polygons
• Twice Q-polynomial distance-regular graphs are thin