Graphs with three distinct \(\alpha\)-eigenvalues

DOI10.1007/s40306-018-0275-yzbMath1402.05142OpenAlexW2809738087MaRDI QIDQ1994056

Muhammad Ateeq Tahir, Xiao Dong Zhang

Publication date: 1 November 2018

Published in: Acta Mathematica Vietnamica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40306-018-0275-y

zbMATH Keywords

strongly regular graphjoin of graphs\(\alpha\)-eigenvalues\(A_{\alpha}\) matrix

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Structural characterization of families of graphs (05C75)

Related Items (6)

On the multiplicity of an arbitrary \(A_\alpha\)-eigenvalue of a connected graph ⋮ The multiplicity of an \(A_\alpha \)-eigenvalue: a unified approach for mixed graphs and complex unit gain graphs ⋮ On the characteristic polynomial of the \(A_\alpha\)-matrix for some operations of graphs ⋮ The \(A_\alpha\)-spread of a graph ⋮ On the least eigenvalue of \(A_\alpha \)-matrix of graphs ⋮ On the multiplicity of \(\alpha\) as an eigenvalue of the \(a_\alpha\) matrix of a graph in terms of the number of pendant vertices

Cites Work

• The spectrum and the signless Laplacian spectrum of coronae
• Universal adjacency matrices with two eigenvalues
• Graphs whose normalized Laplacian has three eigenvalues
• Spectra of graphs
• On graphs with three distinct Laplacian eigenvalues
• Multiplicative cones - a family of three eigenvalue graphs
• Nonregular graphs with three eigenvalues
• Graphs with constant \(\mu\) and \(\overline{\mu}\)
• Which graphs are determined by their spectrum?
• On graphs with three eigenvalues
• A note on graphs whose signless Laplacian has three distinct eigenvalues
• Merging the A-and Q-spectral theories

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