On the multiplicity of \(\alpha\) as an eigenvalue of \(A_\alpha(G)\) of graphs with pendant vertices

DOI10.1016/j.laa.2018.04.013zbMath1391.05282OpenAlexW2802868204MaRDI QIDQ1754425

Germain Pastén, Oscar Rojo, Domingos Moreira Cardoso

Publication date: 30 May 2018

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

Full work available at URL: https://doi.org/10.1016/j.laa.2018.04.013

zbMATH Keywords

eigenvaluesadjacency matrixLaplacian matrixnullitysignless Laplacian matrixconvex combination of matrices

Mathematics Subject Classification ID

Association schemes, strongly regular graphs (05E30) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items (16)

Graphs with eigenvalue \(-1\) of multiplicity \(2 \theta (G)+ \rho (G) -1\) ⋮ On the multiplicity of −1 as an eigenvalue of a tree with given number of pendant vertices ⋮ On the multiplicity of an arbitrary \(A_\alpha\)-eigenvalue of a connected graph ⋮ Bounds for the largest and the smallest \(A_\alpha\) eigenvalues of a graph in terms of vertex degrees ⋮ The multiplicity of an \(A_\alpha \)-eigenvalue: a unified approach for mixed graphs and complex unit gain graphs ⋮ Line graphs of trees with the largest eigenvalue multiplicity ⋮ The \(A_\alpha\)-spread of a graph ⋮ Unnamed Item ⋮ \( A_\alpha\)-spectral characterizations of some joins ⋮ On the least eigenvalue of \(A_\alpha \)-matrix of graphs ⋮ The Nordhaus-Gaddum type inequalities of \(A_\alpha \)-matrix ⋮ Graphs with clusters perturbed by regular graphs -- \(A_\alpha \)-spectrum and applications ⋮ Unnamed Item ⋮ On the multiplicity of \(\alpha\) as an eigenvalue of the \(a_\alpha\) matrix of a graph in terms of the number of pendant vertices ⋮ On the multiplicity of \(\alpha\) as an \(A_\alpha(\varGamma)\)-eigenvalue of signed graphs with pendant vertices ⋮ The multiplicity of an arbitrary eigenvalue of a graph in terms of cyclomatic number and number of pendant vertices

Cites Work

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• Spectra of weighted compound graphs of generalized Bethe trees
• Maximal core size in singular graphs
• Merging the A-and Q-spectral theories
• Eigenvalues and eigenvectors of tridiagonal matrices

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