New results on the \(\mathcal{D}_\alpha\)-matrix of connected graphs

DOI10.1016/j.laa.2019.04.030zbMath1416.05170OpenAlexW2942880020MaRDI QIDQ2002698

Roberto C. Díaz, Oscar Rojo, Germain Pastén

Publication date: 12 July 2019

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

Full work available at URL: https://doi.org/10.1016/j.laa.2019.04.030

zbMATH Keywords

clusterspectral radiusdistance matrixmultipartite graphdistance signless Laplacian matrixH-join

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Distance in graphs (05C12)

Related Items (7)

On the smallest eigenvalue of D_α-matrix of connected graphs ⋮ On spectral radius of the generalized distance matrix of a graph ⋮ The multiplicity of an \(A_\alpha \)-eigenvalue: a unified approach for mixed graphs and complex unit gain graphs ⋮ On Schatten \(p\)-norm of the distance matrices of graphs ⋮ Unnamed Item ⋮ On the minimal \(\mathcal{D}_\alpha -\) spectral radius of graphs subject to fixed connectivity ⋮ The distance Randić matrix of connected graphs

Cites Work

• Edge perturbation on graphs with clusters: adjacency, Laplacian and signless Laplacian eigenvalues
• Two Laplacians for the distance matrix of a graph
• Spectra of graphs
• Laplacian matrices of graphs: A survey
• Commutativity and spectra of Hermitian matrices
• The generalized distance matrix
• Spectra of graphs obtained by a generalization of the join graph operation
• Distance spectra of graphs: a survey
• Large sets of long distance equienergetic graphs
• Merging the A-and Q-spectral theories
• Some properties of the distance Laplacian eigenvalues of a graph

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