A survey of integrity

A communication network can be considered to be highly vulnerable to disruption if the destruction of a few elements can result in no member's being able to communicate with very many others. This idea suggests the concept of the integrity of a graph-the minimum sum of the orders of a set of vertices being removed and a largest remaining component. This survey includes results on the integrity of specific families of graphs and combinations of graphs, relationships with other parameters, bounds, computational complexity, and some variations on the concept. © 1992.