The spectra of the local graphs of the twisted Grassmann graphs

DOI10.1016/j.ejc.2008.07.016zbMath1172.05333OpenAlexW2091852104MaRDI QIDQ1011506

Tatsuya Fujisaki, Jack H. Koolen, Sejeong Bang

Publication date: 8 April 2009

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

Full work available at URL: https://doi.org/10.1016/j.ejc.2008.07.016

zbMATH Keywords

irreducible modulesspectraTerwilliger algebraslocal graphstwisted Grassmann graphs

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (15)

Thin distance-regular graphs with classical parameters \((D, q, q, \frac{q^t-1}{q-1}-1)\) with \(t> D\) are the Grassmann graphs ⋮ Endomorphisms of twisted Grassmann graphs ⋮ Godsil-McKay switching and twisted Grassmann graphs ⋮ Distance-regular graphs of large diameter that are completely regular clique graphs ⋮ Remarks on pseudo-vertex-transitive graphs with small diameter ⋮ Unification of graph products and compatibility with switching ⋮ Graphs with two main and two plain eigenvalues ⋮ The Terwilliger algebra of the twisted Grassmann graph: the thin case ⋮ The Erdős-Ko-Rado theorem for twisted Grassmann graphs ⋮ The Terwilliger polynomial of a \(Q\)-polynomial distance-regular graph and its application to pseudo-partition graphs ⋮ On small world non-Sunada twins and cellular Voronoi diagrams ⋮ Deza graphs based on symplectic spaces ⋮ Recent progress on graphs with fixed smallest adjacency eigenvalue: a survey ⋮ Commutative association schemes ⋮ Thin \(Q\)-polynomial distance-regular graphs have bounded \(c_2\)

Cites Work

• The subconstituent algebra of an association scheme. I
• Some properties of the twisted Grassmann graphs
• The structure of nonthin irreducible \(T\)-modules of endpoint 1: Ladder bases and classical parameters
• The displacement and split decompositions for a \(Q\)-polynomial distance-regular graph
• A new family of distance-regular graphs with unbounded diameter
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