An independent set in a graph is a set of vertices which are pairwise non-adjacent. An independ-ent set of vertices F is a forcing independent set if there is a unique maximum independent set I such that F ⊆ I. The forcing independence number or forcing number of a maximum independent set I is the cardi-nality of a minimum forcing set for I. The forcing number f of a graph is the minimum cardinality of the forcing numbers for the maximum independent sets of the graph. The possible values of f are determined and characterized. We investigate connections between these concepts, other structural concepts, and chemical applications. (doi: 10.5562/cca2295)