This study deals on the concept of (1, 2)-double domination in graphs. Specifically, the study is intended to generate some characterization of this concept for graphs resulting to a binary operation and expose some of the results. This study of domination can be extended into (1, 2)-double domination in graphs. A subset S of V(G) is said to be (1, 2)-double dominating if for every vertex  there are at least two vertices in S one at a distance 1 from v, and the other one at a distance 2 from v. The (1, 2)-double domination number of G, denoted by is the smallest cardinality of the (1, 2)-double dominating set. A (1, 2)-double dominating set of G of cardinality  is then referred to as a -set of G. The main results generated in this study include: (a) characterizations of the (1, 2)-double dominating sets of the join and corona of graphs; (b) bounds or exact values of the (1, 2)-double domination numbers of the join and corona of graphs; and (c) expose some results of (1, 2)-double domination of graphs.

domination, double domination, join, corona.