Vulnerability in Graphs – a Comparative Survey

The concept of tenacity of a graph \(G\) was introduced in References [5,6] as a useful measure of the “vulnerability” of \(G\). In assessing the “vulnerability” of a graph, one determines the extent to which the graph retains certain properties after the removal of vertices or edges. In this paper, we will compare different measures of vulnerability with tenacity for several classes of graphs.