Inverse Independent Outer Connected Domination Number of Few Classes of Graphs

Abstract

In a graph G = (V, E), a vertex set D ⊆ V such that for every vertex v ∈/ D the vertex v is adjacent to atleast one vertex in D and no vertex in D is adjacent to each other, then ,D is the independent dominating set.when the vertex set V D V con- tains a independent dominating set, say D′, then D′ is called the inverse independent domiating set. If the subgraph induced by V − D′ is connected then D′ is called the inverse independent outer connected dominating set. The minimum cardinality of such set of vertices is called the Inverse Independent Outer Connected Domination Number denoted by γ˜I−OC (G). In this paper we will be discussing γ˜I−OC S(n, k), γ˜I−OC S+(n, k), γ˜I−OC S++(n, k), γ˜I−OC (Sn), γ˜I−OC (G1 ◦ G2) where S(n, k), S+(n, k), S++(n, k), Sn are Sierpinski Graph, Extended Sierpinski Graphs and Sierpinski Gasket Graph respectively and G1 and G2 are two standard graphs.