The scattering number of thorn graphs

Abstract

The scattering number of a non-complete connected graph G is defined by sc(G) = max{w(G − S) − |S| : S ⊂ V(G) and w(G − S) ≥ 2}, where w(G − S) denotes the number of components of the graph G − S. If an interconnection network is modelled as a graph, then the scattering number shows not only the difficulty to break down the network but also the damage that has been caused. This article includes several results on the scattering number of thorn graphs as an interconnection network. In addition, the scattering numbers of graphs obtained via various operations are computed. These operations are union and product.

^†E-mail: [email protected]

Keywords:

• Scattering number
• Stability

Notes

^†E-mail: [email protected]