On the \(A_{\alpha}\)-spectra of trees

DOI10.1016/j.laa.2017.01.029zbMath1357.05089arXiv1609.00835OpenAlexW2580704452MaRDI QIDQ513238

Yong-Cai Geng, Sumit K. Garg

Publication date: 3 March 2017

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

Full work available at URL: https://arxiv.org/abs/1609.00835

zbMATH Keywords

treeadjacency matrixgeneralized Bethe treesignless Laplacianconvex combination of matrices

Mathematics Subject Classification ID

Trees (05C05) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18)

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• An explicit formula for eigenvalues of Bethe trees and upper bounds on the largest eigenvalue of any tree
• The spectra of the adjacency matrix and Laplacian matrix for some balanced trees
• Theory of monomer-dimer systems
• On the eigenvalues of trees
• Matrix Analysis
• The Monotonicity Theorem, Cauchy's Interlace Theorem, and the Courant- Fischer Theorem
• Merging the A-and Q-spectral theories

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