Algebraic connectivity of weighted trees under perturbation

DOI10.1080/03081089708818498zbMath0882.05091OpenAlexW2076442060MaRDI QIDQ4366158

Michael Neumann, Stephen J. Kirkland

Publication date: 11 March 1998

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

Full work available at URL: https://doi.org/10.1080/03081089708818498

zbMATH Keywords

positive matricesalgebraic connectivityweighted treePerron value

Mathematics Subject Classification ID

Trees (05C05) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Positive matrices and their generalizations; cones of matrices (15B48) Connectivity (05C40)

Related Items (27)

Perron components and algebraic connectivity for weighted graphs ⋮ A lower bound for the algebraic connectivity of a graph in terms of the domination number ⋮ On algebraic connectivity of graphs with at most two points of articulation in each block ⋮ Trees with matrix weights: Laplacian matrix and characteristic-like vertices ⋮ On the Laplacian spectral radius of trees with fixed diameter ⋮ Old and new results on algebraic connectivity of graphs ⋮ The algebraic connectivity of lollipop graphs ⋮ On the characteristic set, centroid, and centre for a tree ⋮ Combinatorial Perron values of trees and bottleneck matrices ⋮ Minimizing algebraic connectivity over graphs made with some given blocks ⋮ Combinatorial Perron parameters for trees ⋮ The effect on the algebraic connectivity of a tree by grafting or collapsing of edges ⋮ Algebraic connectivity and degree sequences of trees ⋮ A survey of automated conjectures in spectral graph theory ⋮ A tight upper bound on the spectral radius of bottleneck matrices for graphs ⋮ On the Laplacian spectral radius of weighted trees with a positive weight set ⋮ A minimax-condition for the characteristic center of a tree ⋮ The algebraic connectivity of graphs under perturbation ⋮ ALGEBRAIC CONNECTIVITY OF WEIGHED GRAPHS UNDER SHIFTING COMPONENTS ⋮ A conjecture on the algebraic connectivity of connected graphs with fixed girth ⋮ On the Fiedler vectors of graphs that arise from trees by Schur complementation of the Laplacian ⋮ The Laplacian spectra of graphs with a tree structure ⋮ On the Laplacian spectral radius of weighted trees with fixed diameter and weight set ⋮ First eigenvalue and first eigenvectors of a nonsingular unicyclic mixed graph ⋮ On operations in which graphs are appended to trees ⋮ The \(e\)-positivity and Schur positivity of some spiders and broom trees ⋮ Maximizing the distance between center, centroid and characteristic set of a tree

Cites Work

• Eigenvalues, diameter, and mean distance in graphs
• Laplacian matrices of graphs: A survey
• Characteristic vertices of weighted trees via perron values
• The Laplacian Spectrum of a Graph
• Absolute algebraic connectivity of trees
• Ordering trees by algebraic connectivity

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