Excellent γ - stable graphs

Abstract

A graph G is said to be γ – stable if γ ( Gxy ) = γ ( G ), for all x, y ∈ V ( G ), x not adjacent to y, where Gxy denotes the graph obtained by identifying the vertices x, y. In this paper we have obtained conditions under which a graph G is γ - stable and very excellent. We have proved that if G is γ - stable and very excellent, then it is domination subdivision stable. We have obtained method of generating γ - stable graphs when G is γ - stable and just excellent. Properties satisfied by a γ - stable graph having cut vertices are proved.