The Edge-Integrity of Some Graphs

In a communication network, several vulnerability measures are used to determine the resistance of the network to disruption of operation after the failure of certain stations or communication links. If we think of a graph as modeling a network, the edge-integrity of a graph is one \textbf{measure of graph vulnerability} and it is defined to be the minimum sum of the orders of a set of edges being removed and a largest remaining component. In this paper, the edge-integrity of graphs \(B_n\), \(H_n\), and \(E_p^t\), are calculated. Also, some results are given about edge-integrity of these graphs.