Proof of conjecture involving the second largest signless Laplacian eigenvalue and the index of graphs

DOI10.1016/j.laa.2010.12.018zbMath1223.05171OpenAlexW2105462195WikidataQ122925724 ScholiaQ122925724MaRDI QIDQ550616

Kinkar Chandra Das

Publication date: 13 July 2011

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

Full work available at URL: https://doi.org/10.1016/j.laa.2010.12.018

zbMATH Keywords

graphindexsignless Laplacian matrixsecond largest signless Laplacian eigenvalue

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50)

Related Items (11)

On the spectral radius of bipartite graphs which are nearly complete ⋮ On the second largest eigenvalue of the signless Laplacian ⋮ Proof of conjectures involving algebraic connectivity of graphs ⋮ Spectral radius and degree sequence of a graph ⋮ Proof of conjectures on remoteness and proximity in graphs ⋮ Proof of conjectures on the distance signless Laplacian eigenvalues of graphs ⋮ Unnamed Item ⋮ Proof of conjectures involving the largest and the smallest signless Laplacian eigenvalues of graphs ⋮ Nordhaus-Gaddum-type result on the second largest signless Laplacian eigenvalue of a graph ⋮ Some relations between the eigenvalues of adjacency, Laplacian and signless Laplacian matrix of a graph ⋮ The difference between remoteness and radius of a graph

Cites Work

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• 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
• On conjectures involving second largest signless Laplacian eigenvalue of graphs
• The lollipop graph is determined by its \(Q\)-spectrum
• The Laplacian spectrum of a graph
• Hamilton cycles and eigenvalues of graphs
• Eigenvalue bounds for the signless laplacian
• Towards a spectral theory of graphs based on the signless Laplacian, I

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