Computing the Scattering Number of Bicyclic 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 G - X. This parameter can be used to measure the vulnerability of networks. If an interconnection network is modelled as a graph, then the scattering number shows not only the difficulty to break down the network but also the damage that has been caused. This article includes several results on the scattering number of bicyclic graphs and a recursive algorithm for computing the scattering number of bicyclic graphs.