Research on the Domination-Stability of Network G2

It has been known that an interconnection network can be modeled by a connected graph whose vertices represent sites of the network and whose edges represent physical communication links. Being the underlying theory of network, graph theory can be used to investigate network issues. In this paper we consider two parameters of graph: the domination number and bondage number b(G). These parameters measure to some extent the robustness of an interconnection network with respect to link failures. By constructing a family of minimum dominating sets we calculate the domination number and bondage number of graph G(2).