On a conjecture for the signless Laplacian eigenvalues

Bibliography on the Signless Laplacian Eigenvalues

New Theorems for Signless Laplacian Eigenvalues

AMS Mathematics Subject Classification (2000): 05C50

Majorization bounds for signless Laplacian eigenvalues

Ela on the Main Signless Laplacian Eigenvalues of a Graph

A signless Laplacian eigenvalue of a graph G is called a main signless Laplacian eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this paper, some necessary and sufficient conditions for a graph with one main signless Laplacian eigenvalue or two main signless Laplacian eigenvalues are given. And the trees and unicyclic graphs with exactly two main signless L...

On the sum of signless Laplacian eigenvalues of a graph

For a simple graph G, let e(G) denote the number of edges and Sk(G) denote the sum of the k largest eigenvalues of the signless Laplacian matrix of G. We conjecture that for any graph G with n vertices, Sk(G) ≤ e(G) + k+1 2 for k = 1, . . . , n. We prove the conjecture for k = 2 for any graph, and for all k for regular graphs. The conjecture is an analogous to a conjecture by A.E. Brouwer with ...