A measure of graph vulnerability: Scattering number

Abstract

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. Copyright © 2002 Hindawi Publishing Corporation. All rights reserved.