In this paper, we define the notions of inverse split and non split domination in graphs. We get many bounds on inverse split and non split domination numbers. Nordhaus-Gaddum type results are also obtained for these new parameters.Keywords: Independent set, dominating set, split dominating set, non-split dominating set, inverse split dominating set, inverse non-split dominating set, inverse split and non-split domination numbers.

Let G = (V, E) be a simple, finite, undirected graph with V = n and E = m. Kulli introduced the new graph valued function namely the semi-total block graph of a graph G. Let B 1 = {u 1 ,u 2 ,...,u r , r 2} be a block of G. Then we say that the point u 1 and block B 1 are incident with each other, as are u 2 and B 1, u 3 and B 1 and so on. If two distinct blocks B 1 and B 2 are incident with a common cut point then they are called adjacent blocks.

Let G=(V,E) be a simple, finite, connected and undirected graph. A non-empty subset D of V(G) in a graph G=(V,E) is a dominating set if every vertex in V-D is adjacent to atleast one vertex in D. The domination number γ(G) of G is the minimum cardinality of a minimal dominating set of G. A non-empty subset D of V(G) is called an equitable dominating set of a graph G if for every, there exists a vertex such that and . The minimum cardinality of such a minimal dominating set is denoted by γ e (G) and is called an equitable domination number of G. A dominating set D of graph G is called a split dominating set, if the induced subgraph is disconnected. Let denote the greatest integer not greater than and denote the least integer not less than x . In this paper, we investigated the split, inverse and equitable domination number of the middle and the central graphs of the path P n and the cycle C n

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