Distance-regular graphs of large diameter that are completely regular clique graphs

DOI10.1007/s10801-017-0808-9zbMath1401.05319OpenAlexW2779791510MaRDI QIDQ1631384

Hiroshi Suzuki

Publication date: 6 December 2018

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

Full work available at URL: https://doi.org/10.1007/s10801-017-0808-9

zbMATH Keywords

Terwilliger algebradistance-regular graphassociation schemesubconstituent algebracompletely regular codedistance-semiregular graph

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Distance in graphs (05C12) Connectivity (05C40)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Completely regular clique graphs. II
• The twisted Grassmann graph is the block graph of a design
• Edge-distance-regular graphs are distance-regular
• Completely regular clique graphs
• On distance-regular graphs with smallest eigenvalue at least \(- m\)
• Delsarte set graphs with small \(c_{2}\)
• The subconstituent algebra of an association scheme. I
• The subconstituent algebra of an association scheme. III
• The subconstituent algebra of an association scheme. II
• On the maximal cliques of the quadratic forms graph in even characteristic
• Some properties of the twisted Grassmann graphs
• Delsarte clique graphs
• On a new family of (P and Q)-polynomial schemes
• The spectra of the local graphs of the twisted Grassmann graphs
• Association schemes of quadratic forms
• Distance-regular graphs and halved graphs
• The large cliques in the graph of quadratic forms
• A new family of distance-regular graphs and the \(\{ 0,1,2 \}\)-cliques in dual polar graphs
• Completely regular codes
• Alternating bilinear forms over GF(q)
• Bilinear forms over a finite field, with applications to coding theory
• The complete list of maximal cliques of \(\text{Quad}(n,q)\), \(q\) even
• The last subconstituent of a bipartite \(Q\)-polynomial distance-regular graph
• Classification of the maximal cliques of size \(\geq q+4\) in the quadratic forms graph in odd characteristic
• The complete list of maximal cliques of Quad\((n,q)\), \(q\) odd
• The subconstituent algebra of a strongly regular graph
• The Erdős-Ko-Rado theorem for twisted Grassmann graphs
• A new family of distance-regular graphs with unbounded diameter