On the neighbour-integrity of sequential joined graphs

In a communication network, the vulnerability measures the resistance of the network to disruption of operation after the failure of certain stations or communication links. We consider that two graphs have the same connectivity; but the order of their largest components are not equal. Then, these two graph must be different in respect to stability. How can we measure that property? Many graph theoretical parameters have been used in the past to describe the stability of communication networks. New parameters take into account what remains after the graph is disconnected. Several of these deal with the two fundamental questions. How many vertices can still communicate? How difficult is it to reconnect the graph? The neighbour-integrity of a graph is one measure of graph vulnerability. In the neighbour-integrity, it is considered that any failured vertex effects its neighbour vertices. In this work, we consider the neighbour-integrity number of sequential joined graphs that represent communications network. We give the theorems on this classes of graphs