A finite, undirected graph G= (V, E) consists of a finite non – empty set of vertices V = V(G) together with a set E= E(G) of unordered pairs of distinct vertices called edges. A subset D of V(G) is called a strongly equitable dominating set of G if for every v ∈ V- D, there exists atleast one u∈D such that u and v are adjacent also deg(u)≥deg(v), there exists a vertex u∈D such that uv∈E(G) and |deg(u) – deg(v) | ≤ 1. The minimum cardinality of minimal strongly equitable dominating set is called as strongly equitable domination number. It is denoted by γ_se (G) and this D is a split domination set if is disconnected. The non bondage number of a graph, is the cardinality of a maximum number of edges, whose removal (G-E), results in a graph with domination number is equal to a domination number of G and it is denoted by b_nses (G). That is γ_ses (G-E)= γ_ses (G).