International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 1, Pages 1-8
doi:10.1155/S0161171202012607
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 Alpay Kirlangiç. 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.
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.