A measure of graph vulnerability: Scattering number (Q1608152)

Summary: The scattering number of a graph \(G\), denoted \(\text{sc} (G)\), is defined by \(\text{sc} (G)=\max\{ c (G-S)- |S|:S\subseteq V (G)\) and \(c (G-S)\neq 1\}\) 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, the scattering number of a binomial tree is calculated. Also several results are given about binomial trees and graph operations.