AbstractLet G be a graph with n vertices and e(G) edges, and let μ1(G)⩾μ2(G)⩾⋯⩾μn(G)=0 be the Laplacian eigenvalues of G. Let Sk(G)=∑i=1kμi(G), where 1⩽k⩽n. Brouwer conjectured that Sk(G)⩽e(G)+k+12 for 1⩽k⩽n. It has been shown in Haemers et al. [7] that the conjecture is true for trees. We give upper bounds for Sk(G), and in particular, we show that the conjecture is true for unicyclic and bicyclic graphs
We present a general method for proving upper bounds on the eigenvalues of the graph Laplacian. In p...
Let G be a graph of order n with signless Laplacian eigenvalues q(1),...,q(n) and Laplacian eigenval...
AbstractSeveral upper bounds on the largest Laplacian eigenvalue of a graph G, in terms of degree an...
AbstractLet k be a natural number and let G be a graph with at least k vertices. Brouwer conjectured...
If μm and dm denote, respectively, the m-th largest Laplacian eigenvalue and the m-th largest vertex...
AbstractLet G=(V,E) be a simple connected graph and λ1(G) be the largest Laplacian eigenvalue of G. ...
AbstractIn this paper, we obtain the following upper bound for the largest Laplacian graph eigenvalu...
summary:For a simple graph $G$ on $n$ vertices and an integer $k$ with $1\leq k\leq n$, denote by $\...
AbstractLet G=(V,E) be a simple graph on vertex set V={v1,v2,…,vn}. Further let di be the degree of ...
AbstractLet G be a simple graph, its Laplacian matrix is the difference of the diagonal matrix of it...
summary:For a bipartite graph $G$ and a non-zero real $\alpha $, we give bounds for the sum of the...
AbstractFor a graph G and a real number α≠0, the graph invariant sα(G) is the sum of the αth power o...
AbstractGiven an n-vertex graph G=(V,E), the Laplacian spectrum of G is the set of eigenvalues of th...
AbstractLet G be a simple connected weighted graph on n vertices in which the edge weights are posit...
Let G be a simple graph on n vertices and e(G) edges. Consider the signless Laplacian, Q(G) = D + A,...
We present a general method for proving upper bounds on the eigenvalues of the graph Laplacian. In p...
Let G be a graph of order n with signless Laplacian eigenvalues q(1),...,q(n) and Laplacian eigenval...
AbstractSeveral upper bounds on the largest Laplacian eigenvalue of a graph G, in terms of degree an...
AbstractLet k be a natural number and let G be a graph with at least k vertices. Brouwer conjectured...
If μm and dm denote, respectively, the m-th largest Laplacian eigenvalue and the m-th largest vertex...
AbstractLet G=(V,E) be a simple connected graph and λ1(G) be the largest Laplacian eigenvalue of G. ...
AbstractIn this paper, we obtain the following upper bound for the largest Laplacian graph eigenvalu...
summary:For a simple graph $G$ on $n$ vertices and an integer $k$ with $1\leq k\leq n$, denote by $\...
AbstractLet G=(V,E) be a simple graph on vertex set V={v1,v2,…,vn}. Further let di be the degree of ...
AbstractLet G be a simple graph, its Laplacian matrix is the difference of the diagonal matrix of it...
summary:For a bipartite graph $G$ and a non-zero real $\alpha $, we give bounds for the sum of the...
AbstractFor a graph G and a real number α≠0, the graph invariant sα(G) is the sum of the αth power o...
AbstractGiven an n-vertex graph G=(V,E), the Laplacian spectrum of G is the set of eigenvalues of th...
AbstractLet G be a simple connected weighted graph on n vertices in which the edge weights are posit...
Let G be a simple graph on n vertices and e(G) edges. Consider the signless Laplacian, Q(G) = D + A,...
We present a general method for proving upper bounds on the eigenvalues of the graph Laplacian. In p...
Let G be a graph of order n with signless Laplacian eigenvalues q(1),...,q(n) and Laplacian eigenval...
AbstractSeveral upper bounds on the largest Laplacian eigenvalue of a graph G, in terms of degree an...
DOI
Add to ORKG