Combinatorial designs with two singular values. I: Uniform multiplicative designs

DOI10.1016/j.jcta.2004.04.004zbMath1048.05017OpenAlexW3122615815MaRDI QIDQ598442

van Dam, Edwin R., Spence, Edward

Publication date: 6 August 2004

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.2004.04.004

zbMATH Keywords

Singular valuesBipartite graphs with four eigenvaluesMultiplicative designs

Mathematics Subject Classification ID

Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Statistical block designs (62K10)

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Bi-Cayley normal uniform multiplicative designs ⋮ On regular graphs with four distinct eigenvalues ⋮ On graphs with three distinct signless Laplacian eigenvalues ⋮ Maximum order of graphs with a given corank ⋮ On 2-equitable graphs ⋮ On signed graphs with at most two eigenvalues unequal to \(\pm 1\) ⋮ The signed graphs with two eigenvalues unequal to \(\pm 1\) ⋮ The non-bipartite graphs with all but two eigenvalues in [–1, 1] ⋮ Which graphs are determined by their spectrum? ⋮ On optimality of designs with three distinct eigenvalues ⋮ Graphs with four distinct Laplacian eigenvalues ⋮ Bipartite graphs with five eigenvalues and pseudo designs ⋮ Combinatorial designs with two singular values. II: Partial geometric designs ⋮ On the spectrum of an extremal graph with four eigenvalues ⋮ Quantum walks on embeddings ⋮ Developments on spectral characterizations of graphs ⋮ The characterization of graphs with eigenvalue -1 of multiplicity n-4 or n-5 ⋮ The graphs with all but two eigenvalues equal to \(\pm 1\)

Cites Work

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• Tactical decompositions in uniform normal designs
• Rational congruence for uniform multiplicative designs
• Multiplicative designs I: The normal and reducible cases
• Multiplicative designs II. Uniform normal and related structures
• The existence of symmetric block designs
• Multiplicative cones - a family of three eigenvalue graphs
• Nonregular graphs with three eigenvalues
• Small regular graphs with four eigenvalues
• Combinatorial designs with two singular values. II: Partial geometric designs
• A nonregular analogue of conference graphs
• Regular graphs with four eigenvalues
• On the replications of certain multiplicative designs
• Symmetric designs and related configurations