A set D of vertices in a graph G = (V, E) is a nonsplit dominating set if the induced subgraph V − D is connected. The minimum cardinality of a nonsplit dominating set is called the nonsplit domination number of G and is denoted γ ns (G). The nonsplit bondage number of a central graph b ns (C(G)) is the minimum cardinality of a set E of edges for which γ ns (C(G) − E) > γ ns (C(G)). In this paper, we obtain the nonsplit domination number of central graph (γ ns (C(G))) and the bondage number of central graph (b ns (C(G))) are obtained for some standard graphs.