Summary: Let \(G=(V,E)\) be a graph and \(\mathcal{K}\) be a family of subset of \(V\) whose union is \(V\). A hub set \(H\) of \(G\) is a \(\mathcal{K}\)-hub set if \(H\cap K\ne\varphi\) for every \(K\in\mathcal{K}\). The minimum cardinality of such \(H\) is the \(\mathcal{K}\)-hub number of \(G\) and in denoted by \(h_{\mathcal{K}}(G)\). In this paper we study some results of this parameter.