Vulnerability in graphs: the neighbour-integrity of line graphs

Abstract

The vulnerability of a graph is a determination that includes certain properties of the graph not to be damaged after the removal of a number of vertices or edges. One measure of vulnerability to vertex removal is neighbour-integrity. The vertex-neighbour-integrity is a measure of the vulnerability of graphs to disruption caused by the removal of vertices and all of their adjacent vertices. In this article we consider vertex removal and give some results on the neighbour-integrity of line graphs.

Keywords:

• Vulnerability
• Communication network
• Graph theory
• Connectivity
• Neighbour-integrity