Modified Types of Triple Effect Domination

Abstract

Let  be a finite, simple and undirected graph without isolated vertices. A sub set  is a triple effect dominating set, if every vertex in  dominates exactly three vertices of . Triple effect domination number  is the minimum cardinality over all triple effect dominating sets in . A subset  of V-D is an inverse triple effect dominating set if every v?  dominates exactly three vertices of V? . The inverse triple effect domination number (G) is the minimum cardinality over all inverse triple effect dominating sets in . In this papers, total, independent, co-independent, connected and doubly connected triple effect domination are introduced with their inverse as a modified of the triple effect domination. Several properties and bounds are given and proved. Then, these modified dominations are applied on some graphs.