Let  be a simple graph. A subset S of  is an outer-connected 2-dominating set of G if S is a 2-dominating set of G and the graph  is connected. The outer-connected 2‑domination number of G, denoted by  is the smallest cardinality of an outer-connected 2-dominating set of G. In this paper, we characterize the outer-connected 2-dominating sets of the join, corona, and lexicographic product of graphs. As direct consequences, the corresponding bounds or exact values of the outer-connected 2-domination numbers of these graphs are obtained.

2-domination, outer-connected, join, corona, lexicographic product.