Oriented gain graphs, line graphs and eigenvalues

DOI10.1016/j.laa.2016.05.040zbMath1346.05103arXiv1506.05059OpenAlexW2963157799MaRDI QIDQ739113

Nathan Reff

Publication date: 17 August 2016

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

Full work available at URL: https://arxiv.org/abs/1506.05059

zbMATH Keywords

voltage graphgain graphcomplex unit gain graphline graph eigenvaluesorientation on gain graphsoriented gain graph

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Signed and weighted graphs (05C22) Graph operations (line graphs, products, etc.) (05C76)

Related Items (22)

Characterizations of line graphs in signed and gain graphs ⋮ Unit gain graphs with two distinct eigenvalues and systems of lines in complex space ⋮ On the relation between the adjacency rank of a complex unit gain graph and the matching number of its underlying graph ⋮ On the adjacency matrix of a complex unit gain graph ⋮ Unnamed Item ⋮ The multiplicity of an \(A_\alpha \)-eigenvalue: a unified approach for mixed graphs and complex unit gain graphs ⋮ Mixed graphs whose Hermitian adjacency matrices of the second kind have the smallest eigenvalue greater than \(- \frac{3}{2}\) ⋮ On the \({A_{\!\mathbb{C}}}\)-rank of multidigraphs ⋮ Incidence matrices and line graphs of mixed graphs ⋮ Characterizing signed mixed graphs with small eigenvalues ⋮ NEPS of complex unit gain graphs ⋮ Bounds for the energy of a complex unit gain graph ⋮ Gain-line graphs via \(G\)-phases and group representations ⋮ Laplacian matrices of general complex weighted directed graphs ⋮ Spectra of quaternion unit gain graphs ⋮ Bounds for the extremal eigenvalues of gain Laplacian matrices ⋮ Unnamed Item ⋮ A group representation approach to balance of gain graphs ⋮ Balancedness and the least Laplacian eigenvalue of some complex unit gain graphs ⋮ Spectral fundamentals and characterizations of signed directed graphs ⋮ The \(k\)-generalized Hermitian adjacency matrices for mixed graphs ⋮ Hermitian adjacency matrix of the second kind for mixed graphs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spectral integral variation and unicyclic 3-colored digraphs with second smallest eigenvalue 1
• Spectral properties of complex unit gain graphs
• On weighted directed graphs
• Balance in gain graphs - a spectral analysis
• Biased graphs. I: Bias, balance, and gains
• Signed graphs represented by \(D_{\infty}\)
• Orientation of signed graphs
• Signed graphs with least eigenvalue \(<-2\)
• Line graphs, root systems, and elliptic geometry
• Biased graphs IV: Geometrical realizations
• A characterization of signed graphs represented by root system \(D_ \infty\)
• Universal state transfer on graphs
• On the Laplacian coefficients of signed graphs
• A reciprocal eigenvalue property for unicyclic weighted directed graphs with weights from \(\{\pm 1,{\pm}i\}\)
• Acyclic orientations of graphs
• On the spectrum of 3-coloured digraphs
• Matrices in the Theory of Signed Simple Graphs
• On colored digraphs with exactly one nonsingular cycle
• Signed Graphs and Geometry
• Oriented Matroids
• EMBEDDINGS OF COMPLEX LINE SYSTEMS AND FINITE REFLECTION GROUPS

This page was built for publication: Oriented gain graphs, line graphs and eigenvalues