Sharp upper and lower bounds for largest eigenvalue of the Laplacian matrices of trees
From MaRDI portal
Publication:2487982
DOI10.1016/J.DISC.2005.04.001zbMath1068.05044OpenAlexW1986098644MaRDI QIDQ2487982
Publication date: 17 August 2005
Published in: Discrete Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.disc.2005.04.001
Related Items (98)
A note on upper bounds for the spectral radius of weighted graphs ⋮ On the spectral radius and energy of digraphs ⋮ The spanning k-trees, perfect matchings and spectral radius of graphs ⋮ Bounds for the (Laplacian) spectral radius of graphs with parameter α ⋮ Signless Laplacian spectral radius of graphs without short cycles or long cycles ⋮ On incidence energy of a graph ⋮ On the spectral radius and the energy of a digraph ⋮ Extremal Halin graphs with respect to the signless Laplacian spectra ⋮ Walks and the spectral radius of graphs ⋮ Minimizing the Laplacian eigenvalues for trees with given domination number ⋮ Sharp upper bounds on the \(Q\)-index of (minimally) 2-connected graphs with given size ⋮ Maximizing the signless Laplacian spectral radius of \(k\)-connected graphs with given diameter ⋮ Laplacian spectral radius and maximum degree of trees with perfect matchings ⋮ Bounds on the (Laplacian) spectral radius of graphs ⋮ Unnamed Item ⋮ A bound on the spectral radius of graphs in terms of their Zagreb indices ⋮ Inequalities for the number of walks in graphs ⋮ Some upper bounds for the energy of graphs ⋮ On upper bounds for the energy of digraphs ⋮ Walks and eigenvalues of signed graphs ⋮ Maxima of the \(Q\)-index: graphs with no \(K_{1,t}\)-minor ⋮ Ordering \(Q\)-indices of graphs: given size and circumference ⋮ Maxima of the \(Q\)-spectral radius of \(C_3 (C_4)\)-free graphs with given size and minimum degree \(\delta \geq 2\) ⋮ Matrix power inequalities and the number of walks in graphs ⋮ Spectral analogues of Erdős’ and Moon–Moser’s theorems on Hamilton cycles ⋮ Bounds on the independence number and signless Laplacian index of graphs ⋮ Maxima of the \(Q\)-index of non-bipartite graphs: forbidden short odd cycles ⋮ Extremal (balanced) blow-ups of trees with respect to the signless Laplacian index ⋮ On the spectral radius of trees with given independence number ⋮ Sufficient spectral conditions for graphs being k-edge-Hamiltonian or k-Hamiltonian ⋮ The Laplacian spectral radii of unicyclic and bicyclic graphs with \(n\) vertices and \(k\) pendant vertices ⋮ On the signless Laplacian index of cacti with a given number of pendant vertices ⋮ The \(Q\)-minimizer graph with given independence number ⋮ Maxima of the \(Q\)-index of non-bipartite \(C_3\)-free graphs ⋮ The least eigenvalue of the signless Laplacian of the complements of trees ⋮ On a conjecture for the signless Laplacian spectral radius of cacti with given matching number ⋮ Bounds on the eigenvalues of graphs with cut vertices or edges ⋮ Some graft transformations and its applications on the distance spectral radius of a graph ⋮ Stability of Woodall's theorem and spectral conditions for large cycles ⋮ Spectral radius conditions for fractional \([a,b\)-covered graphs] ⋮ The smallest signless Laplacian spectral radius of graphs with a given clique number ⋮ Lower bounds for the Laplacian energy of bipartite graphs ⋮ Unnamed Item ⋮ On the signless Laplacian index of unicyclic graphs with fixed diameter ⋮ A conjecture on the diameter and signless Laplacian index of graphs ⋮ On ordering bicyclic graphs with respect to the Laplacian spectral radius ⋮ On the signless Laplacian spectra of \(k\)-trees ⋮ The effect on the adjacency and signless Laplacian spectral radii of uniform hypergraphs by grafting edges ⋮ Note on the \(k\)th Laplacian eigenvalues of trees with perfect matchings ⋮ Ordering trees with \(n\) vertices and matching number \(q\) by their largest Laplacian eigenvalues ⋮ Sharp upper and lower bounds for the Laplacian spectral radius and the spectral radius of graphs ⋮ The signless Laplacian or adjacency spectral radius of bicyclic graphs with given number of cut edges ⋮ Maximize the \(Q\)-index of graphs with fixed order and size ⋮ Laplacian spectral radius of trees with given maximum degree ⋮ Answers to Gould's question concerning the existence of chorded cycles ⋮ On the signless Laplacian index and radius of graphs ⋮ On sum of powers of the Laplacian eigenvalues of graphs ⋮ Unnamed Item ⋮ Bounds for the extreme eigenvalues of the Laplacian and signless Laplacian of a graph ⋮ The Laplacian spectral radius of trees and maximum vertex degree ⋮ On the Laplacian spectral radius of weighted trees with a positive weight set ⋮ The signless Laplacian spectral radius of tricyclic graphs and trees with \(k\) pendant vertices ⋮ Bounds and conjectures for the signless Laplacian index of graphs ⋮ On the Laplacian spectral radii of bipartite graphs ⋮ On the Laplacian spectral radius of bipartite graphs with fixed order and size ⋮ On the weighted trees with given degree sequence and positive weight set ⋮ Bounds for the Laplacian spectral radius of graphs ⋮ The minimum signless Laplacian spectral radius of graphs with given independence number ⋮ On the signless Laplacian spectral radius of graphs with cut vertices ⋮ The Laplacian spectral radius for unicyclic graphs with given independence number ⋮ Measure-theoretic bounds on the spectral radius of graphs from walks ⋮ Chromatic number and spectral radius ⋮ The \(Q\)-index and connectivity of graphs ⋮ Maxima of the \(Q\)-index of leaf-free graphs with given size ⋮ The Laplacian spectral radius of a graph under perturbation ⋮ Maxima of the Q ( L )-index of (minimally) 2-edge-connected graphs with given size ⋮ Lower bounds on the (Laplacian) spectral radius of weighted graphs ⋮ Spectral sufficient conditions for graph factors containing any edge ⋮ On the sum of powers of Laplacian eigenvalues of bipartite graphs ⋮ On the sum of powers of Laplacian eigenvalues of bipartite graphs ⋮ On the Laplacian spectral radius of weighted trees with fixed diameter and weight set ⋮ An edge-grafting theorem on Laplacian spectra of graphs and its application ⋮ Maximizing the Laplacian spectral radii of graphs with given diameter ⋮ Energy of nonsingular graphs: improving lower bounds ⋮ The majorization theorems of single-cone trees and single-cone unicyclic graphs ⋮ On the spectral radius of weighted trees with fixed diameter and weight set ⋮ The Laplacian spectral radius of some graphs ⋮ The Laplacian spectral radius of tricyclic graphs with \(n\) vertices and \(k\) pendant vertices ⋮ Maximizing the signless Laplacian spectral radius of graphs with given diameter or cut vertices ⋮ On the Laplacian spectral radii of trees with perfect matchings ⋮ Sharp bounds on the signless Laplacian spread of graphs ⋮ The signless Laplacian spectral radius of graphs with given number of pendant vertices ⋮ On the Laplacian spectral radii of trees ⋮ Ordering graphs with given size by their signless Laplacian spectral radii ⋮ Minimizing the Laplacian spectral radius of trees with given matching number ⋮ Bounds for the Laplacian spectral radius of graphs ⋮ The second least eigenvalue of the signless Laplacian of the complements of trees ⋮ Upper bounds on the smallest positive eigenvalue of trees with at most one zero eigenvalue
Cites Work
- Unnamed Item
- Unnamed Item
- Laplacian matrices of graphs: A survey
- Bounds on eigenvalues and chromatic numbers
- On the Laplacian spectral radius of a tree.
- On the spectral radius of graphs
- A sharp upper bound on the largest eigenvalue of the Laplacian matrix of a graph
- On the spectral radius of graphs with cut vertices
- Spectral Radius and Degree Sequence
This page was built for publication: Sharp upper and lower bounds for largest eigenvalue of the Laplacian matrices of trees
