AbstractA biclique in a graph Γ is a complete bipartite subgraph of Γ. We give bounds for the maximum number of edges in a biclique in terms of the eigenvalues of matrix representations of Γ. These bounds show a strong similarity with Lovász's bound ϑ(Γ) for the Shannon capacity of Γ. Motivated by this similarity we investigate bicliques and the bounds in certain product graphs
AbstractLet G a simple undirected graph with n ⩾ 2 vertices and let α0(G) ⩾ …, αn−1(G) be the eigenv...
AbstractGernert conjectured that the sum of two largest eigenvalues of the adjacency matrix of any s...
Let μ1 (G) ≥ ... ≥ μn (G) be the eigenvalues of the adjacency matrix of a graph G of order n, and Ḡ ...
AbstractA biclique in a graph Γ is a complete bipartite subgraph of Γ. We give bounds for the maximu...
We prove that the maximum edge biclique problem in bipartite graphs is NP-complete.A biclique in a b...
AbstractWe prove that the maximum edge biclique problem in bipartite graphs is NP-complete
AbstractConnected graphs in which the number of edges equals the number of vertices plus one are cal...
AbstractThe Hermitian rank, h(A), of a Hermitian matrix A is defined and shown to equal max{n+(A),n−...
A biclique of a graph G is a maximal induced complete bipar tite subgraph of G. Given a graph G, the...
AbstractThe largest eigenvalue of the adjacency matrix of a graph has received considerable attentio...
AbstractUpper and lower estimates are found for the maximum of the kth eigenvalue of a graph as a fu...
AbstractWe consider the general problem of determining the maximum possible multiplicity of an eigen...
AbstractWe show that every limit point of the kth largest eigenvalues of graphs is a limit point of ...
The largest eigenvalue of the adjacency matrix of a graph has received considerable attention in the...
AbstractWe give new bounds on eigenvalue of graphs which imply some known bounds. In particular, if ...
AbstractLet G a simple undirected graph with n ⩾ 2 vertices and let α0(G) ⩾ …, αn−1(G) be the eigenv...
AbstractGernert conjectured that the sum of two largest eigenvalues of the adjacency matrix of any s...
Let μ1 (G) ≥ ... ≥ μn (G) be the eigenvalues of the adjacency matrix of a graph G of order n, and Ḡ ...
AbstractA biclique in a graph Γ is a complete bipartite subgraph of Γ. We give bounds for the maximu...
We prove that the maximum edge biclique problem in bipartite graphs is NP-complete.A biclique in a b...
AbstractWe prove that the maximum edge biclique problem in bipartite graphs is NP-complete
AbstractConnected graphs in which the number of edges equals the number of vertices plus one are cal...
AbstractThe Hermitian rank, h(A), of a Hermitian matrix A is defined and shown to equal max{n+(A),n−...
A biclique of a graph G is a maximal induced complete bipar tite subgraph of G. Given a graph G, the...
AbstractThe largest eigenvalue of the adjacency matrix of a graph has received considerable attentio...
AbstractUpper and lower estimates are found for the maximum of the kth eigenvalue of a graph as a fu...
AbstractWe consider the general problem of determining the maximum possible multiplicity of an eigen...
AbstractWe show that every limit point of the kth largest eigenvalues of graphs is a limit point of ...
The largest eigenvalue of the adjacency matrix of a graph has received considerable attention in the...
AbstractWe give new bounds on eigenvalue of graphs which imply some known bounds. In particular, if ...
AbstractLet G a simple undirected graph with n ⩾ 2 vertices and let α0(G) ⩾ …, αn−1(G) be the eigenv...
AbstractGernert conjectured that the sum of two largest eigenvalues of the adjacency matrix of any s...
Let μ1 (G) ≥ ... ≥ μn (G) be the eigenvalues of the adjacency matrix of a graph G of order n, and Ḡ ...
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