Maximal digraphs whose Hermitian spectral radius is at most 2

DOI10.1016/j.laa.2022.11.007zbMath1504.05163arXiv2109.09114OpenAlexW3200672812MaRDI QIDQ2104985

Alexander L. Gavrilyuk, Akihiro Munemasa

Publication date: 8 December 2022

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

Full work available at URL: https://arxiv.org/abs/2109.09114

zbMATH Keywords

eigenvaluedigraphroot systemHermitian matrixDynkin diagramintegral lattice

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Signed and weighted graphs (05C22)

Cites Work

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• Line graphs, root systems, and elliptic geometry
• On mixed graphs whose Hermitian spectral radii are at most 2
• Cyclotomic matrices over the Eisenstein and Gaussian integers
• Digraphs with Hermitian spectral radius below 2 and their cospectrality with paths
• Large regular bipartite graphs with median eigenvalue 1
• Integer symmetric matrices having all their eigenvalues in the interval \([ - 2,2\)]
• Class numbers of definite Hermitian forms
• Equiangular lines
• Lattices and Codes
• Signed analogue of line graphs and their smallest eigenvalues

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