A valency bound for distance-regular graphs

DOI10.1016/j.jcta.2017.11.008zbMath1377.05052OpenAlexW2768398866MaRDI QIDQ1689048

Zhi Qiao, Jack H. Koolen

Publication date: 12 January 2018

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2017.11.008

zbMATH Keywords

distance-regular graphssmallest eigenvalue3-chromaticvalency bound

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Coloring of graphs and hypergraphs (05C15) Distance in graphs (05C12)

Related Items (5)

A new characterization of the dual polar graphs ⋮ Non-bipartite distance-regular graphs with a small smallest eigenvalue ⋮ Fractional decompositions and the smallest-eigenvalue separation ⋮ On 2-walk-regular graphs with a large intersection number \(c_2\) ⋮ Non-bipartite distance-regular graphs with diameters 5, 6 and a smallest eigenvalue

Cites Work

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• Distance-regular graphs
• On distance-regular graphs with smallest eigenvalue at least \(- m\)
• The nonexistence of regular near octagons with parameters \((s,t,t_2,t_3)=(2,24,0,8)\)
• The structure of near polygons with quads
• There exists no distance-regular graph with intersection array \((5,4,3;1,1,2)\)
• A Higman-Haemers inequality for thick regular near polygons
• Chromatic number and the 2-rank of a graph
• Light tails and the Hermitian dual polar graphs
• On 3-chromatic distance-regular graphs
• Strongly regular graphs with (-1, 1, 0) adjacency matrix having eigenvalue 3

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