Results on the integrity of double star graphs

A network begins losing nodes or links, or there may be a loss in its effectiveness. Thus, the communication network must be constructed to be as stable as possible, not only with respect to the initial disruption, but also with respect to the possible reconstruction of the network. Stability numbers of a communication network measure its durability with respect to a break down. If we consider a graph as modelling of a communication network, connectivity is an important measure of reliability or stability of a graph, but not enough. Integrity is a new measurement of stability. It takes into consideration the number of vertices of the remaining components after some disruption. Also the edge-integrity is defined. In this paper, we study integrity (or vertex-integrity) and edge-integrity of Double Star Graphs and some of its compounds