AbstractLet k be a natural number and let G be a graph with at least k vertices. Brouwer conjectured that the sum of the k largest Laplacian eigenvalues of G is at most e(G)+k+12, where e(G) is the number of edges of G. We prove this conjecture for k=2. We also show that if G is a tree, then the sum of the k largest Laplacian eigenvalues of G is at most e(G)+2k-1
We show that if μj is the j-th largest Laplacian eigenvalue, and dj is the j-th largest degree (1 j ...
We show that if µj is the jth largest Laplacian eigenvalue, and dj is the jth largest degree (1 = j ...
Let G be a simple graph on n vertices and e(G) edges. Consider the signless Laplacian, Q(G) = D + A,...
AbstractLet G be a graph with n vertices and e(G) edges, and let μ1(G)⩾μ2(G)⩾⋯⩾μn(G)=0 be the Laplac...
AbstractLet k be a natural number and let G be a graph with at least k vertices. Brouwer conjectured...
AbstractGiven an n-vertex graph G=(V,E), the Laplacian spectrum of G is the set of eigenvalues of th...
The Laplacian energy of a graph is the sum of the distances of the eigenvalues of the Laplacian matr...
AbstractThis paper is concerned with techniques for quantitative analysis of the largest p-Laplacian...
If μm and dm denote, respectively, the m-th largest Laplacian eigenvalue and the m-th largest vertex...
AbstractLet G be a simple graph with n vertices. The matrix L(G)=D(G)−A(G) is called the Laplacian o...
AbstractGernert conjectured that the sum of two largest eigenvalues of the adjacency matrix of any s...
A Teoria Espectral de Grafos é um ramo da Matemática Discreta que se preocupa com a relação entre as...
AbstractSeveral upper bounds on the largest Laplacian eigenvalue of a graph G, in terms of degree an...
We show several sharp upper and lower bounds for the sum of the largest eigenvalues of the signless ...
AbstractLet G be a simple graph, its Laplacian matrix is the difference of the diagonal matrix of it...
We show that if μj is the j-th largest Laplacian eigenvalue, and dj is the j-th largest degree (1 j ...
We show that if µj is the jth largest Laplacian eigenvalue, and dj is the jth largest degree (1 = j ...
Let G be a simple graph on n vertices and e(G) edges. Consider the signless Laplacian, Q(G) = D + A,...
AbstractLet G be a graph with n vertices and e(G) edges, and let μ1(G)⩾μ2(G)⩾⋯⩾μn(G)=0 be the Laplac...
AbstractLet k be a natural number and let G be a graph with at least k vertices. Brouwer conjectured...
AbstractGiven an n-vertex graph G=(V,E), the Laplacian spectrum of G is the set of eigenvalues of th...
The Laplacian energy of a graph is the sum of the distances of the eigenvalues of the Laplacian matr...
AbstractThis paper is concerned with techniques for quantitative analysis of the largest p-Laplacian...
If μm and dm denote, respectively, the m-th largest Laplacian eigenvalue and the m-th largest vertex...
AbstractLet G be a simple graph with n vertices. The matrix L(G)=D(G)−A(G) is called the Laplacian o...
AbstractGernert conjectured that the sum of two largest eigenvalues of the adjacency matrix of any s...
A Teoria Espectral de Grafos é um ramo da Matemática Discreta que se preocupa com a relação entre as...
AbstractSeveral upper bounds on the largest Laplacian eigenvalue of a graph G, in terms of degree an...
We show several sharp upper and lower bounds for the sum of the largest eigenvalues of the signless ...
AbstractLet G be a simple graph, its Laplacian matrix is the difference of the diagonal matrix of it...
We show that if μj is the j-th largest Laplacian eigenvalue, and dj is the j-th largest degree (1 j ...
We show that if µj is the jth largest Laplacian eigenvalue, and dj is the jth largest degree (1 = j ...
Let G be a simple graph on n vertices and e(G) edges. Consider the signless Laplacian, Q(G) = D + A,...
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