On conjectures involving second largest signless Laplacian eigenvalue of graphs

DOI10.1016/j.laa.2010.01.005zbMath1195.05040OpenAlexW2080062770WikidataQ122903963 ScholiaQ122903963MaRDI QIDQ967519

Kinkar Chandra Das

Publication date: 29 April 2010

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

Full work available at URL: https://doi.org/10.1016/j.laa.2010.01.005

zbMATH Keywords

graphLaplacian matrixalgebraic connectivitysignless Laplacian matrixthe largest signless Laplacian eigenvaluesmallest signless Laplacian eigenvaluethe second largest signless Laplacian eigenvalue

Mathematics Subject Classification ID

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

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Cites Work

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• Completion of Laplacian integral graphs via edge addition
• Combinatorial properties and the complexity of a max-cut approximation
• The performance of an eigenvalue bound on the max-cut problem in some classes of graphs
• Signless Laplacians of finite graphs
• Q-integral graphs with edge-degrees at most five
• A sharp lower bound for the least eigenvalue of the signless Laplacian of a non-bipartite graph
• A survey of automated conjectures in spectral graph theory
• Bounds on the \(Q\)-spread of a graph
• The signless Laplacian spectral radius of graphs with given degree sequences
• The lollipop graph is determined by its \(Q\)-spectrum
• On the Laplacian eigenvalues of a graph
• Laplacian matrices of graphs: A survey
• A new upper bound for eigenvalues of the Laplacian matrix of a graph
• An improved upper bound for Laplacian graph eigenvalues
• A characterization on graphs which achieve the upper bound for the largest Laplacian eigenvalue of graphs.
• The Laplacian spectrum of a graph
• Expanding and forwarding
• Sharp lower bounds on the Laplacian eigenvalues of trees
• Sharp upper bounds for the Laplacian graph eigenvalues
• Hamilton cycles and eigenvalues of graphs
• Research problems from the Aveiro workshop on graph spectra
• Eigenvalue bounds for the signless laplacian
• Maximizing spectral radius of unoriented Laplacian matrix over bicyclic graphs of a given order
• On the conjecture for certain Laplacian integral spectrum of graphs
• Towards a spectral theory of graphs based on the signless Laplacian, I
• Rank one perturbation and its application to the laplacian spectrum of a graph^∗
• The Laplacian Spectrum of a Graph II
• On graphs whose Laplacian matrices have distinct integer eigenvalues
• Matrix theory. Basic results and techniques

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