On the number of integral graphs

DOI10.1016/j.laa.2015.11.027zbMath1329.05186OpenAlexW2252257822MaRDI QIDQ905735

Parker Williams, Kevin P. Costello

Publication date: 28 January 2016

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2015.11.027

zbMATH Keywords

random matrixgraph spectrumintegral eigenvalue

Mathematics Subject Classification ID

Random graphs (graph-theoretic aspects) (05C80) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Random matrices (algebraic aspects) (15B52)

Related Items (2)

Bipartite graphs with all but two eigenvalues equal to \(0\) and \(\pm 1\) ⋮ Recent progress in combinatorial random matrix theory

Cites Work

• Inverse Littlewood-Offord problems and the singularity of random symmetric matrices
• On the distribution of the roots of certain symmetric matrices
• Perfect state transfer in integral circulant graphs
• Random symmetric matrices are almost surely nonsingular.
• Graphs with integral spectrum
• On subspaces spanned by random selections of \(\pm 1\) vectors
• Random matrices have simple spectrum
• Invertibility of symmetric random matrices
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