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 $c(G-S)-|S|$ 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.