Solutions for two conjectures on the eigenvalues of the eccentricity matrix, and beyond

DOI10.1016/j.disc.2020.111925zbMath1441.05150OpenAlexW3015468551WikidataQ123140239 ScholiaQ123140239MaRDI QIDQ2185928

Wei Wei, Shuchao Li, Xiaocong He

Publication date: 8 June 2020

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2020.111925

zbMATH Keywords

spectral radiusdiameterleast eigenvalueeccentricity matrix

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Distance in graphs (05C12)

Related Items (17)

On the eccentricity spectra of complete multipartite graphs ⋮ On the eccentricity matrices of trees: inertia and spectral symmetry ⋮ On the eigenvalues of eccentricity matrix of graphs ⋮ Characterizing the extremal graphs with respect to the eccentricity spectral radius, and beyond ⋮ On the spectral radius and the energy of eccentricity matrices of graphs ⋮ On the least eccentricity eigenvalue of graphs ⋮ Extremal problems for the eccentricity matrices of complements of trees ⋮ Some properties on eccentricity matrices of uniform hypertrees ⋮ Eccentricity spectral radius of \(t\)-clique trees with given diameter ⋮ On the eccentricity energy and eccentricity spectral radius of graphs with odd diameter ⋮ On graphs with exactly one anti-adjacency eigenvalue and beyond ⋮ Energy and inertia of the eccentricity matrix of coalescence of graphs ⋮ On the largest and least eigenvalues of eccentricity matrix of trees ⋮ On the eccentricity spectra of threshold graphs ⋮ The eccentricity matrix of a digraph ⋮ Some extremal problems on the distance involving peripheral vertices of trees with given matching number ⋮ Spectral determination of graphs with one positive anti-adjacency eigenvalue

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• Extremal Halin graphs with respect to the signless Laplacian spectra
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• The anti-adjacency matrix of a graph: eccentricity matrix
• Distance spectra of graphs: a survey
• Graph energy based on the eccentricity matrix
• On the spectral characterizations of graphs

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