Relationships between scattering number and other vulnerability parameters

Let G be a non-complete connected graph. The scattering number of G is defined as s(G) = max{ω(G - X) - |X|: X ⊂ V(G), ω(G - X) > 1], where ω(G - X) is the number of components of G - X. This parameter can be used to measure the vulnerability of networks. It shows not only the difficulty to break down the network but also the damage that has been caused. In this article, the relationships between the scattering number and some other vulnerability parameters, namely the toughness, integrity and tenacity, are established. Examples show that the results are the best possible.