A collection that is edge disjoint and all of its edges belong to is referred to as a decomposition of. It is referred to as a primedecomposition of if every graph is a prime graph. . The minimum cardinality among the minimal ID set is called an ID number ofG(V,E)and it is denoted by? ?(G).Further study the inverse domination number? ?(G).of complete and complete bipartite IFGsome results and also identify some bounds of the ID-number are investigated. The ID-number of some standard operations join of two IFGsand Cartesian product of two IFG are investigated. Some results likeG(V,E)is an IFG without isolated vertices, then? (G) ?? ?(G).The IFGG(V,E)be a complete IFG, thenG u if ??? ( ), here u is the vertex having the second minimum cardinality inG(V,E).AnIFGG(A,B)be a complete bipartite IFG, thenG u v if ? ??? ( ), here u and v are the vertex having the second minimumcardinality in vertices set 1 2 V and VinG(V,E)
