Construction of integral graphs

The integrity of a graph G = (V; E) is dened as I(G) = minfjSj + m(G S) : S V (G)g, where m(G X) denotes the order of the largest component in the graph G X. This is a better parameter to measure the stability of a network G; as it takes into account both the amount of work done to damage the network and how badly the net-work is damaged. In this paper, the maximum networks are obtained with prescribed order and integrity, and a method for constructing this sort of networks is also presented. Fi-nally, we give the trees of minimum integrity with given order and maximum degree