. Semigraph is a pair where is a nonempty set whose elements are called vertices of and is a set of ordered n-tuples called edges of . A Semigraph called bipartite semigraph if its vertex set can be partitioned into set such that and are independent sets. A set is a dominating set of if adjacent with . If there is not exist is a dominating set such that is a minimal dominating set of and minimum cardinality of a minimal dominating set is called the domination number of and it is denoted by . A set is a hyper dominating set of if hyper dominated by . If there is not exist is hyper dominating set such that is a minimal hyper dominating set of and minimum cardinality of a minimal hyper dominating set is called the hyper...