On point-set domination in graphs IV: Separable graphs with unique minimum psd-sets Original Research Article

A set D of vertices in a graph G = (V,E) is called a point-set dominating (or, psd-) set of G if for every nonempty subset S of V − D there exists v ϵ D such that the induced subgraph 〈S ∪ {v}〉 is connected (cf. Sampthkumar and Pushpa Latha (1993) [6]). Here, we report results of our investigation into the nature of connected separable graphs having unique minimum psd-sets. In particular, we characterize block-cactus graphs (with at least two blocks) having this property.