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A set S⊆ V(G) said to be an at most twin outer perfect dominating set if for every vertex v∈V-S, l⩽|N(v)∩S|⩽2 and   has at least one perfect matching. The minimum cardinality of at most twin outer perfect dominating set is called the at most twin outer perfect domination number and  γ atop ( G ) denotes this number. This was initiated by G.Mahadevan.et.al., recently. Here we find this number for general Binary-tree. corona product of paths and cycles and lotus inside graph.

EXPLORING AT MOST TWIN OUTER PERFECT DOMINATION NUMBER FOR GENERAL BINARY TREE AND SOME SPECIAL GRAPHS