The Nonsplit Bondage Number of Graphs - Chrislight, R. Jemimal; Mary, Y. Therese Sunitha (International Journal of Computer Sciences and Engineering, 2025)
A set of vertices in a graph is a nonsplit dominating set if the induced subgraph is connected. The minimum cardinality of a nonsplit dominating set is called the nonsplit domination number of and denoted . In this paper, we define the nonsplit bondage number of a graph to be the minimum cardinality of a set of edges for which . We obtain sharp bounds for and obtain the exact values for some standard graphs.