A graph G is said to be γ- stable if γ (Gxy) = γ (G), for all x, y ∈ V (G), x is not adjacent to y, where Gxy denotes the graph obtained by merging the vertices x, y. In this paper we have provided a necessary and sufficient condition for G¯ to be γ- stable, where G¯ denotes the complement of G. We have obtained a characterization of planar graphs when G and G¯ are γ- stable graphs.