“…On the other hand, lots of natural graph parameters are defined as the number of vertex or edge subsets of a certain kind; we mention, for example, the number of independent vertex subsets [15,18], the number of matchings [7], the number of dominating or efficient dominating sets [2,3] or the number of subtrees [13,21]. Some of them play an important role in applications as well, for instance the number of matchings that is known as Hosoya index in mathematical chemistry [9,12] and is also connected to the monomer-dimer model of statistical physics [10].…”