Inverse Domination Number and Inverse Total Domination of Sierpinski Star Graph

Given a graph G= (V (G), E (G) ) consisting of the set of vertices V (G) and the set of edges E (G). For example, D (G) is a domination set of graph G with minimum cardinality, if V (G) -D (G) contains a domination set D^ (-1) (G), then D^ (-1) (G) is called the inverse domination set of graph G. The minimum cardinality of the inverse domination set of the graph G is called the inverse domination number, denoted by γ^ (-1) (G). If Dₜ (G) is the total domination set of the graph G with minimal cardinality, and V (G) -Dₜ (G) contains the total domination set Dₜ^ (-1) (G), then Dₜ^ (-1) (G) is called the inverse total domination set of the graph G. The minimum cardinality of the inverse total domination set of the graph G is called the inverse total domination number, denoted by γₜ^ (-1) (G). This paper discusses the inverse domination and the inverse total domination on the Sierpinski Star graph SSₙ, obtained the inverse domination number γ^ (-1) (SSₙ) =0 for n<3 and γ^ (-1) (SSₙ) =4∙3^ (n-3) for n≥3 and the inverse total domination number γₜ^ (-1) (SSₙ) =0 for n≥1.