Abstract Let G be a simple connected graph and S 2 ( G ) $S_{2}(G)$ be the sum of the two largest Laplacian eigenvalues of G. In this paper, we determine the bicyclic graph with maximum S 2 ( G ) $S_{2}(G)$ among all bicyclic graphs of order n, which confirms the conjecture of Guan et al. (J. Inequal. Appl. 2014:242, 2014) for the case of bicyclic graphs
We show several sharp upper and lower bounds for the sum of the largest eigenvalues of the signless ...
We show that if μj is the j-th largest Laplacian eigenvalue, and dj is the j-th largest degree (1 j ...
Gernert conjectured that the sum of two largest eigenvalues of the adjacency matrix of any simple gr...
Let G be a simple graph on n vertices and e(G) edges. Consider the signless Laplacian, Q(G) = D + A,...
AbstractLet k be a natural number and let G be a graph with at least k vertices. Brouwer conjectured...
AbstractLet G be a simple connected graph with n vertices and m edges. Denote the degree of vertex v...
AbstractGernert conjectured that the sum of two largest eigenvalues of the adjacency matrix of any s...
AbstractLet G be a simple graph with n vertices. The matrix L(G)=D(G)−A(G) is called the Laplacian o...
AbstractLet G be a simple graph. Let λ1(G) and μ1(G) denote the largest eigenvalue of the adjacency ...
AbstractWe study extremal graphs for the extremal values of the second largest Q-eigenvalue of a con...
AbstractLet G=(V,E) be a simple connected graph and λ1(G) be the largest Laplacian eigenvalue of G. ...
AbstractLet G=(V,E) be a simple graph. Denote by D(G) the diagonal matrix of its vertex degrees and ...
AbstractLet G be a graph with n vertices and e(G) edges, and let μ1(G)⩾μ2(G)⩾⋯⩾μn(G)=0 be the Laplac...
AbstractIn this paper, we obtain the following upper bound for the largest Laplacian graph eigenvalu...
Let $G$ be a simple connected graph and let $S_k(G)$ be the sum of the first $k$ largest signless La...
We show several sharp upper and lower bounds for the sum of the largest eigenvalues of the signless ...
We show that if μj is the j-th largest Laplacian eigenvalue, and dj is the j-th largest degree (1 j ...
Gernert conjectured that the sum of two largest eigenvalues of the adjacency matrix of any simple gr...
Let G be a simple graph on n vertices and e(G) edges. Consider the signless Laplacian, Q(G) = D + A,...
AbstractLet k be a natural number and let G be a graph with at least k vertices. Brouwer conjectured...
AbstractLet G be a simple connected graph with n vertices and m edges. Denote the degree of vertex v...
AbstractGernert conjectured that the sum of two largest eigenvalues of the adjacency matrix of any s...
AbstractLet G be a simple graph with n vertices. The matrix L(G)=D(G)−A(G) is called the Laplacian o...
AbstractLet G be a simple graph. Let λ1(G) and μ1(G) denote the largest eigenvalue of the adjacency ...
AbstractWe study extremal graphs for the extremal values of the second largest Q-eigenvalue of a con...
AbstractLet G=(V,E) be a simple connected graph and λ1(G) be the largest Laplacian eigenvalue of G. ...
AbstractLet G=(V,E) be a simple graph. Denote by D(G) the diagonal matrix of its vertex degrees and ...
AbstractLet G be a graph with n vertices and e(G) edges, and let μ1(G)⩾μ2(G)⩾⋯⩾μn(G)=0 be the Laplac...
AbstractIn this paper, we obtain the following upper bound for the largest Laplacian graph eigenvalu...
Let $G$ be a simple connected graph and let $S_k(G)$ be the sum of the first $k$ largest signless La...
We show several sharp upper and lower bounds for the sum of the largest eigenvalues of the signless ...
We show that if μj is the j-th largest Laplacian eigenvalue, and dj is the j-th largest degree (1 j ...
Gernert conjectured that the sum of two largest eigenvalues of the adjacency matrix of any simple gr...
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