A measure of graph vulnerability: scattering number - Alpay Kirlangiç (International Journal of Mathematics and Mathematical Sciences)
The scattering number of a graph G, denoted sc(G), is defined by sc(G)=max{c(G−S)−|S|:S⫅V(G)    and   c(G−S)≠1} where c(G−S) denotes the number of components in G−S. It is one measure of graph vulnerability. In this paper, general results on the scattering number of a graph are considered. Firstly, some bounds on the scattering number are given. Further, scattering number of a binomial tree is calculated. Also several results are given about binomial trees and graph operations.