The Fibonacci Cube is an interconnection network that gets many desirable properties that are very important in the network design, network stability and applications. The extended Fibonacci Cube is a new network topology. The vulnerability value of a communication network shows the resistance of the network after the disruption of some centres or connection lines until the communication breakdown. In a network, as the number of centres belonging to sub networks changes, the vulnerability of the network also changes and requires greater degrees of stability or less vulnerability. If the communication network is modelled by graph G, the deterministic measures tend to provide a worst-case analysis of some aspects of overall disconnection process. Many graph theoretical parameters have been used in the past to describe the stability of communication networks. There are few parameters such as integrity, neighbour-integrity and, tenacity number, giving the vulnerability. Also, in the neighbour-integrity, if a station is destroyed, the adjacent stations will be betrayed so that the betrayed stations become useless to network as a whole.