Using symbolic computation to prove nonexistence of distance-regular graphs

zbMath1401.05320arXiv1803.10797MaRDI QIDQ1991433

Janoš Vidali

Publication date: 30 October 2018

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.10797

zbMATH Keywords

nonexistencedistance-regular graphssymbolic computationtriple intersection numbersKrein parameters

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30)

Related Items (8)

Implications of vanishing Krein parameters on Delsarte designs, with applications in finite geometry ⋮ On tight 4-designs in Hamming association schemes ⋮ On few-class Q-polynomial association schemes: feasible parameters and nonexistence results ⋮ On some recent progress in the classification of (\(P\) and \(Q\))-polynomial association schemes ⋮ Computing distance-regular graph and association scheme parameters in \texttt{SageMath} with \texttt{sage}-\texttt{drg} ⋮ sage-drg ⋮ A survey of semisimple algebras in algebraic combinatorics ⋮ Inverse problems in the class of distance-regular graphs of diameter 4

Uses Software

• Mathematica
• Maxima
• SageMath
• Python

Cites Work

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• Distance-regular graphs
• Bipartite distance-regular graphs: the \(Q\)-polynomial property and pseudo primitive idempotents
• Triple intersection numbers of \(Q\)-polynomial distance-regular graphs
• Extremal 1-codes in distance-regular graphs of diameter 3
• Using equality in the Krein conditions to prove nonexistence of certain distance-regular graphs
• Strongly regular graphs having strongly regular subconstituents
• A new condition for distance-regular graphs
• Some elementary inequalities for distance-regular graphs
• Tight distance-regular graphs
• Restrictions on classical distance-regular graphs
• Taut distance-regular graphs and the subconstituent algebra
• Examples of computer experimentation in algebraic combinatorics

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