On distance-regular graphs with fixed valency

DOI10.1007/BF01788534zbMath0626.05050WikidataQ105583185 ScholiaQ105583185MaRDI QIDQ580374

Tatsuro Ito, Eiichi Bannai

Publication date: 1987

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

zbMATH Keywords

distance-regular graphdiameter

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Graph theory (05C99)

Related Items (16)

Two-geodesic transitive graphs of valency six ⋮ Two theorems concerning the Bannai-Ito conjecture ⋮ On distance-regular graphs with \(k_ i= k_ j\). II ⋮ A constant bound on the number of columns \((1,k-2,1)\) in the intersection array of a distance-regular graph ⋮ On distance-regular graphs with fixed valency. III ⋮ On distance-regular graphs with fixed valency. IV ⋮ A bound for the number of columns \(\ell_{(c,a,b)}\) in the intersection array of a distance-regular graph ⋮ On distance-regular graphs with fixed valency. II ⋮ There are only finitely many distance-regular graphs of fixed valency greater than two ⋮ On geodesic transitive graphs ⋮ Bounding the diameter of a distance regular graph by a function of \(k_ d\) ⋮ There are only finitely many regular near polygons and geodetic distance-regular graphs with fixed valency ⋮ Current research on algebraic combinatorics. Supplements to our book, Algebraic combinatorics I ⋮ There are finitely many triangle-free distance-regular graphs with degree 8, 9 or 10 ⋮ Distance-regular graphs of valency 6 and \(a_1=1\) ⋮ On a conjecture of Bannai and Ito: There are finitely many distance-regular graphs with degree 5, 6 or 7

Cites Work

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• Eigenvalue multiplicities of highly symmetric graphs
• Bipartite distance-regular graphs of valency three
• On bipartite tetra0alent graphs
• On the Sims Conjecture and Distance Transitive Graphs
• On Trivalent Graphs

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