On nested split graphs whose second largest eigenvalue is less than 1

DOI10.1016/j.laa.2008.11.026zbMath1194.05098OpenAlexW2038233950MaRDI QIDQ1014485

Zoran Stanić

Publication date: 29 April 2009

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

Full work available at URL: https://doi.org/10.1016/j.laa.2008.11.026

zbMATH Keywords

adjacency matrixsecond largest eigenvaluenested split graphsdivisor technique

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (17)

A note on the Nordhaus-Gaddum type inequality to the second largest eigenvalue of a graph ⋮ Eigenvalue location in graphs of small clique-width ⋮ No threshold graphs are cospectral ⋮ Connected \((K_4 - e)\)-free graphs whose second largest eigenvalue does not exceed 1 ⋮ On the spectrum of threshold graphs ⋮ An explicit formula for the distance characteristic polynomial of threshold graphs ⋮ The A_α-spectral radius of dense graphs ⋮ On tricyclic graphs whose second largest eigenvalue does not exceed 1 ⋮ Characterization of outerplanar graphs whose second largest eigenvalue is at most 1 ⋮ Eigenvalue location in threshold graphs ⋮ Unnamed Item ⋮ Graphs with least eigenvalue \(-2\): ten years on ⋮ Efficient computation of the characteristic polynomial of a threshold graph ⋮ Spectral characterization of unicyclic graphs whose second largest eigenvalue does not exceed 1 ⋮ On regular graphs and coronas whose second largest eigenvalue does not exceed 1 ⋮ On graphs whose second largest eigenvalue is at most 1 ⋮ The \(A_\alpha\)-spectral radius of complements of bicyclic and tricyclic graphs with \(n\) vertices

Cites Work

• On graphs whose second largest eigenvalue equals 1 -- the star complement technique
• The rank of a cograph
• On unicyclic graphs whose second largest eigenvalue does not exceed 1
• On bicyclic graphs whose second largest eigenvalue does not exceed 1
• On regular graphs and coronas whose second largest eigenvalue does not exceed 1
• A Linear Recognition Algorithm for Cographs
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