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International Journal of Mathematics and Mathematical Sciences
Volume 30, Issue 1, Pages 1-8

A measure of graph vulnerability: scattering number

Department of Mathematics, Ege University, Bornova-Izmir 35100, Turkey

Received 2 April 2001; Revised 20 August 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The scattering number of a graph G, denoted sc(G), is defined by sc(G)=max{c(GS)|S|:SV(G) andc(GS)1} where c(GS) denotes the number of components in GS. 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.