Scattering number in graphs
The scattering number of a noncomplete connected graph G is defined by s(G) = max{omega (G - X) - \X\: X subset of V(G), w(G - X) greater than or equal to 2}, where omega (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. (C) 2001 John Wiley & Sons, Inc.
scattering number nordhaus-gaddum-type result toughness integrity