Bounds for the largest and the smallest \(A_\alpha\) eigenvalues of a graph in terms of vertex degrees

DOI10.1016/j.laa.2019.12.039zbMath1437.05151OpenAlexW2998217045WikidataQ126405614 ScholiaQ126405614MaRDI QIDQ2174489

Dein Wong, Fenglei Tian, Sai Wang

Publication date: 21 April 2020

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

Full work available at URL: https://doi.org/10.1016/j.laa.2019.12.039

zbMATH Keywords

spectral radius\( A_\alpha\)-spectrum of graphsthe smallest eigenvalue

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Vertex degrees (05C07)

Related Items (15)

On the smallest eigenvalue of D_α-matrix of connected graphs ⋮ Ordering graphs by their largest (least) A_α-eigenvalues ⋮ On the Aα-spectral radius of connected graphs ⋮ On the \(A_\sigma\)-spectral radii of graphs with some given parameters ⋮ On the characteristic polynomial of the \(A_\alpha\)-matrix for some operations of graphs ⋮ Bounds for A_α-eigenvalues ⋮ Aα-spectrum of duplicate and corona operations in graphs ⋮ Sharp bounds on the \(A_{\alpha}\)-index of graphs in terms of the independence number ⋮ The \(A_\alpha\)-spread of a graph ⋮ Unnamed Item ⋮ Some spectral inequalities for connected bipartite graphs with maximum \(A_\alpha\)-index ⋮ Unnamed Item ⋮ An arithmetic criterion for graphs being determined by their generalized \(A_\alpha \)-spectra ⋮ Aα and Lα-spectral properties of spider graphs ⋮ Some bounds on the A_α-index of connected graphs with fixed order and size

Cites Work

• The clique number and the smallest \(Q\)-eigenvalue of graphs
• A note on the positive semidefiniteness of \(A_{\alpha}(G)\)
• On the \(A_{\alpha}\)-spectra of trees
• The smallest eigenvalue of the signless Laplacian
• Spectra of graphs
• Graphs determined by their \(A_\alpha\)-spectra
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• The \(A_{\alpha}\) spectral radius characterization of some digraphs
• On the \(\alpha\)-index of graphs with pendent paths
• On the \(A_\alpha\)-spectral radius of a graph
• On the multiplicity of \(\alpha\) as an eigenvalue of \(A_\alpha(G)\) of graphs with pendant vertices
• A note on the \(A_{\alpha}\)-spectral radius of graphs
• On the multiplicity of \(\alpha\) as an \(A_\alpha(\varGamma)\)-eigenvalue of signed graphs with pendant vertices
• Eigenvalues of the Laplacian of a graph^∗
• A characterization of the smallest eigenvalue of a graph
• On the α-spectral radius of graphs
• Merging the A-and Q-spectral theories

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