Research on the Total Bondage Number of a Spectial Network

In this paper we consider the total bondage number b_t(G) for Generalized Petersen graphs, which is defined as the minimum number of edges whose removal results in a new graph with larger total domination number. This parameter measures to some extent the robustness of an interconnection network with respect to link failures. Generalized Petersen graphs are an important class of commonly used interconnection networks and have been studied recently. By constructing a family of minimum total dominating sets we compute the total bondage number of the Generalized Petersen graphs.