The nonsplit bondage number of middle graph

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 denoted γns(G). The nonsplit bondage number of a middle graph bns(M(G)) is the minimum cardinality of a set E of edges for which γns(M(G) E)>γns(M(G)). In this paper, γns(M(G)) and bns(M(G)) are obtained for some standard graphs and its bounds are found.