Proof of conjectures on the distance signless Laplacian eigenvalues of graphs

DOI10.1016/j.laa.2014.11.008zbMath1304.05091OpenAlexW2080519708WikidataQ123346217 ScholiaQ123346217MaRDI QIDQ477750

Kinkar Chandra Das

Publication date: 9 December 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.2014.11.008

zbMATH Keywords

second largest eigenvaluedistance signless Laplacian matrixdistance signless Laplacian spectral radius

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Distance in graphs (05C12)

Related Items (25)

NEW BOUNDS AND EXTREMAL GRAPHS FOR DISTANCE SIGNLESS LAPLACIAN SPECTRAL RADIUS ⋮ Characterization of extremal graphs from distance signless Laplacian eigenvalues ⋮ Distance (signless) Laplacian spectral radius of uniform hypergraphs ⋮ The effect of graft transformations on distance signless Laplacian spectral radius ⋮ On generalized distance spectral radius and generalized distance energy of graphs ⋮ On the second largest eigenvalue of the generalized distance matrix of graphs ⋮ Unnamed Item ⋮ Unnamed Item ⋮ On the multiplicity of distance signless Laplacian eigenvalues of graphs ⋮ Bounds on the entries of the principal eigenvector of the distance signless Laplacian matrix ⋮ On distance signless Laplacian spectrum of the complements of unicyclic graphs and trees ⋮ On the distance and distance signless Laplacian spectral radii of tricyclic graphs ⋮ On (distance) Laplacian energy and (distance) signless Laplacian energy of graphs ⋮ Unnamed Item ⋮ Bounds on maximal and minimal entries of the \(p\)-normalized principal eigenvector of the distance and distance signless Laplacian matrices of graphs ⋮ Unnamed Item ⋮ Relation between the matching number and the second largest distance Laplacian eigenvalue of a graph ⋮ Lower bounds of distance Laplacian spectral radii of \(n\)-vertex graphs in terms of matching number ⋮ Matching number, connectivity and eigenvalues of distance signless Laplacians ⋮ On the distance \(\alpha \)-spectral radius of a connected graph ⋮ On distance Laplacian and distance signless Laplacian eigenvalues of graphs ⋮ Distance signless Laplacian eigenvalues of graphs ⋮ On distance signless Laplacian spectrum and energy of graphs ⋮ On the D_α-spectra of graphs ⋮ Distance (signless) Laplacian eigenvalues of \(k\)-uniform hypergraphs

Uses Software

• Mathematica

Cites Work

• Proof of conjecture involving the second largest signless Laplacian eigenvalue and the index of graphs
• Conjectures on index and algebraic connectivity of graphs
• Proof of conjectures involving the largest and the smallest signless Laplacian eigenvalues of graphs
• On conjectures involving second largest signless Laplacian eigenvalue of graphs
• On the distance and distance signless Laplacian spectral radii of bicyclic graphs
• On the distance signless Laplacian of a graph
• On the distance signless Laplacian spectral radius of graphs
• Unnamed Item
• Unnamed Item

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