The influence of Miroslav Fiedler on spectral graph theory

DOI10.1016/j.laa.2012.03.003zbMath1282.05145OpenAlexW1979821251MaRDI QIDQ389537

Vladimir Nikiforov

Publication date: 21 January 2014

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

Full work available at URL: https://doi.org/10.1016/j.laa.2012.03.003

zbMATH Keywords

elliptic matrixalgebraic connectivityFiedler vectoradditive compound matrix

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (7)

Null decomposition of unicyclic graphs ⋮ The geometry connectivity of hypergraphs ⋮ Ordering trees and graphs with few cycles by algebraic connectivity ⋮ A Fiedler-like theory for the perturbed Laplacian ⋮ Localization of dominant eigenpairs and planted communities by means of Frobenius inner products ⋮ Algebraic connectivity of k-connected graphs ⋮ Obituary: Miroslav Fiedler (1926--2015).

Cites Work

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• \(\lambda_ 1\), isoperimetric inequalities for graphs, and superconcentrators
• Spectral partitioning works: planar graphs and finite element meshes
• Old and new results on algebraic connectivity of graphs
• The spectral radius of graphs without paths and cycles of specified length
• The asymptotic behaviour of Fiedler's algebraic connectivity for random graphs
• Elliptic matrices with zero diagonal
• Elliptic matrices and their eigenpolynomials
• Algebraic connectivity may explain the evolution of gene regulatory networks
• Isoperimetric numbers of graphs
• Explicit Concentrators from Generalized N-Gons
• Additive compound matrices and an inequality for eigenvalues of symmetric stochastic matrices
• Extremizing algebraic connectivity subject to graph theoretic constraints
• Spectral radius and Hamiltonicity of graphs

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