Vertex-Neighbor-Scattering Number of Graphs

Abstract

Incorporating the concept of the scattering number and the idea of the vertex-neighbor-connectivity, we introduce a new graph parameter called the vertex-neighbor-scattering number, which measures how easily a graph can be broken into many components with the removal of the neighborhoods of few vertices, and discuss some properties of this parameter. Some tight upper and lower bounds for
this parameter are also given.