Among all other graph parameters, graph integrity is a well-known measure of the vulnerability of the network. The effectiveness of the network decreases with the breaking down of some vertices or links. Therefore, a less vulnerable communication network is required for greater stability. Vulnerability is the measure of the resistance of the network after the failure of communication links. A new vulnerability parameter, domination integrity of fuzzy graph is defined to study the stability and domination property of fuzzy graphs. In this paper, we studied the concept of domination integrity in IFGs and investigated some of its properties. We also introduced domination weak integrity in the IFG and studied some of the results.
