Scattering number in graphs

Abstract

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. © 2001 John Wiley & Sons, Inc.