Bicliques and Eigenvalues

A 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 Lovászʹs bound ϑ(Γ) for the Shannon capacity of Γ. Motivated by this similarity we investigate bicliques and the bounds in certain product graphs.