Independence in direct-product graphs (Q2713636)

By \(\alpha (G)\) the independence number of a graph \(G\) (the maximum number of vertices of an independent set in \(G\)) is denoted; \(G\times H\) denotes the direct product of the graphs \(G, H\). The symbol \(\underline {\alpha }(G\times H) = \max (\alpha (G) \cdot |H|, \alpha (H) \cdot |G|)\) where \(|G|\) and \(|H|\) are the numbers of vertices of \(G\) and \(H\), is introduced. It is investigated, when \(\alpha (G\times H) = \underline {\alpha } (G\times H)\).