A set S of vertices of a connected graph G is a 2-point-set dominating set if for every there is a nonempty containing at most two vertices such that the induced subgraph  of G is connected. If, in addition, for every  there is a adjacent to u for which  is a 2-point-set dominating set of G, then S is a secure 2-point-set dominating set. This paper initiates the study of secure 2-point-set domination in graphs. It characterizes 2-point-set dominating sets and secure 2-point-set dominating sets in both the join and corona of graphs, and, as a result, determines  the values of their respective corresponding point-set domination invariants.

2-point-set dominating set, secure 2-point-set dominating set, 2-point-set domination number, secure 2-point-set domination number.