On -gain graphs with few positive eigenvalues

DOI10.1080/03081087.2022.2120596zbMath1530.05111MaRDI QIDQ6064152

Li-Hua Feng, Xiaocong He, Lu Lu

Publication date: 12 December 2023

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

zbMATH Keywords

spectrumsigned graphmixed graph\(\mathbb{T}_4\)-gain graph

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18)

Cites Work

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• Hermitian-adjacency matrices and Hermitian energies of mixed graphs
• Mixed graphs with \(H\)-rank 3
• Inertia of complex unit gain graphs
• Signed graphs with cut points whose positive inertia indexes are two
• Relations between the inertia indices of a mixed graph and those of its underlying graph
• Characterizing the mixed graphs with exactly one positive eigenvalue and its application to mixed graphs determined by their \(H\)-spectra
• Complex unit gain graphs with exactly one positive eigenvalue
• The negative tetrahedron and the first infinite family of connected digraphs that are strongly determined by the Hermitian spectrum
• Large regular bipartite graphs with median eigenvalue 1
• Signed graphs with small positive index of inertia
• Relation between the inertia indices of a complex unit gain graph and those of its underlying graph
• Characterization of graphs with exactly two non-negative eigenvalues

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