On a conjecture of Bannai and Ito: There are finitely many distance-regular graphs with degree 5, 6 or 7

DOI10.1006/eujc.2002.0609zbMath1012.05160OpenAlexW2090733274MaRDI QIDQ1864611

Jack H. Koolen, Vincent L. Moulton

Publication date: 18 March 2003

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

Full work available at URL: https://doi.org/10.1006/eujc.2002.0609

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30)

Related Items (5)

Two theorems concerning the Bannai-Ito conjecture ⋮ A bound for the number of columns \(\ell_{(c,a,b)}\) in the intersection array of a distance-regular graph ⋮ There are only finitely many distance-regular graphs of fixed valency greater than two ⋮ There are only finitely many regular near polygons and geodetic distance-regular graphs with fixed valency ⋮ There are finitely many triangle-free distance-regular graphs with degree 8, 9 or 10

Cites Work

• On distance-regular graphs with fixed valency
• On distance-regular graphs with fixed valency. II
• Distance-biregular graphs with 2-valent vertices and distance regular line graphs
• On distance-regular graphs with fixed valency. III
• On distance-regular graphs with fixed valency. IV
• Eigenvalue multiplicities of highly symmetric graphs
• The distance-regular graphs of valency four
• An improvement of the Boshier-Nomura bound
• Problems in algebraic combinatorics
• Distance-regular graphs of valency 6 and \(a_1=1\)
• Distance-regular graphs with \(\Gamma(x) \simeq 3* K_{a+1}\)
• Cubic Distance-Regular Graphs
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