A note on extremal values of the scattering number

Abstract

Let c(H) denote the number of components of graph H. The scattering number of a graph G is the maximum of c(G - S) - {pipe}S{pipe} taken over all cut-sets S of G. In this note we explore the minimum and maximum scattering number for several families. For example, we show that the minimum scattering number of a triangle-free graph on n vertices is approximately -n/3. We also consider the scattering number of some graph products.