Criticality of outer - connected independence upon edge removal

In a graph G=(V,E) (not necessarily be connected) an independent set S⊆V is said to be an outer connected independent set if ω(G−S)≤ω(G), where ω(G) is the number of components in G. The maximum cardinality of an outer connected independent set is called the outer connected independence number and it is denoted by Ioc(G). This concept was introduced in [I. Sahul Hamid, R. Gnanaprahasam, M. Fatima Mary Outer Connected Independence in Graphs, Discrete Math, Algorithm, Appl Vol. 7, No. 3 1550039 (2015) [11 pages] DOI]. This paper examine the effect of Ioc when G is modified by deleting an edge.