Integrity of graph operations

A communication network can be considered to be highly vulnerable to disruption if the failure of few members (nodes or links) can result in no members being able to communicate with very many others. These communication networks can be modeled through graphs. There are several graph-theoretic parameters to describe the stability of graphs. But, these parameters are not sufficient to study stability of graphs. This leads to the concept of integrity of a graph. In this paper, we obtain the integrity of some graph operations and some special graphs which can help us to reconstruct the given network in such a way that it is more stable than the earlier one.