A subset S of  in a graph G is said to be a dual-perfect dominating set if every vertex  is adjacent to exactly two vertices in S. The dual-perfect domination number of G, denoted by  is the smallest cardinality of the dual-perfect dominating set of G. Any dual-perfect dominating set of G of cardinality  is then referred to as a -set of G. This study focuses mainly on the dual-perfect domination in graphs. Specifically, this study is geared to generate results out of the following objectives: (a) to characterize the dual-perfect dominating sets on some graphs; and (b) to determine exact values or bounds of the dual-perfect domination numbers of the join and corona of graphs.

domination, dual-perfect, perfect, join, corona.