Domination and Power Domination in Certain Families of Nanostars Dendrimers

Dendrimers are hyper-branched macromolecules having various applications in diverse fields like supra-molecular chemistry, drug delivery and nanotechnology etc. The certain graph invariants such as dominating number and power dominating number can be used to characterize large number of physical properties like physio-chemical properties, thermodynamic properties, chemical and biological activities, etc. A subset of a simple undirected graph is called dominating set if every vertex of the given graph is either in that set or is adjacent to some vertex in that set. The minimum number of elements in that kind of set is called domination number. A subset of the vertex set of a graph G is said to be power dominating set (PDS) of {G} , if every vertex and every edge in G is observed by P. The minimum cardinality of P of a graph G is called power domination number. In this paper, the domination number and power domination number of some nanostars dendrimers have been determined.