Scattering number in graphs

The scattering number of a noncomplete connected graph G is defined by s(G) = max{ω(G - X) - [X]: X ⊂ V(G), ω(G - X) ≥ 2}, where ω(G - X) denotes the number of components of the graph G - X. In this paper, we show that this parameter can be used to measure the vulnerability of a graph. To some extent, it represents a trade-off between the amount of work done to damage the network and how badly the network is damaged. The relationship between the scattering number and some other parameters of a graph is discussed. Furthermore, we give the Nordhaus-Gaddum-type result for scattering number.