Given a graph consisting of the set of vertices and the set of edges . For example, is a domination set of graph with minimum cardinality, if contains a domination set , then is called the inverse domination set of graph . The minimum cardinality of the inverse domination set of the graph is called the inverse domination number, denoted by . If is the total domination set of the graph with minimal cardinality, and contains the total domination set , then is called the inverse total domination set of the graph . The minimum cardinality of the inverse total domination set of the graph is called the inverse total domination number, denoted by . This paper discusses the inverse domination and the inverse total domination on the Sierpinski Star graph , obtained the inverse domination number for and for and the inverse total domination number for .
Keywords: Sierpinski star graph, inverse domination, inverse total domination
