On the two conjectures of Graffiti

DOI10.1016/j.laa.2003.12.014zbMath1051.05062OpenAlexW2157128881WikidataQ122924012 ScholiaQ122924012MaRDI QIDQ1827512

Xiao Dong Zhang

Publication date: 6 August 2004

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

Full work available at URL: https://doi.org/10.1016/j.laa.2003.12.014

zbMATH Keywords

Laplacian eigenvalueIndependence numberTreeGraffiti's conjecture

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69)

Related Items (11)

The Laplacian spread of graphs ⋮ Minimizing the Laplacian eigenvalues for trees with given domination number ⋮ Old and new results on algebraic connectivity of graphs ⋮ The Laplacian spectral radii of trees with degree sequences ⋮ The six classes of trees with the largest algebraic connectivity ⋮ On the Laplacian spectral radius of weighted trees with a positive weight set ⋮ On the weighted trees with given degree sequence and positive weight set ⋮ The Laplacian spectral radius for unicyclic graphs with given independence number ⋮ Trees with a large Laplacian eigenvalue multiplicity ⋮ A relative bound for independence ⋮ Bounds for the Laplacian spectral radius of graphs

Cites Work

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• Some eigenvalue properties in graphs (conjectures of Graffiti -- II)
• Laplacian matrices of graphs: A survey
• A new upper bound for eigenvalues of the Laplacian matrix of a graph
• On the spectral radius of graphs with cut vertices
• Computers and discovery in algebraic graph theory
• On trees with perfect matchings
• The Laplacian Spectrum of a Graph
• The Laplacian Spectrum of a Graph II
• Ordering trees by algebraic connectivity

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