Vulenrability measures in graphs

The vulnerabilty is the resistance of the network to disruption of operation after the failure of certain stations or communication links in a communication network. A communication network can be modelled by a graph as stations corresponding to vertices of graph and communication links corresponding to edges of graph. For measure the vulnerability of graph, many measurement defined such as Connectivity, Integrity, Scattering Number, Rupture Degree, Thoughness and their edge and neighbor analogous. In first section, concept of vulnerability and basic definitions are given. Then some of vulnerability measures and some results in the literatüre related to these measurements are given. In second section, the middle graphs of B_n,E_p^t,H_n^2 are obtained and the domination integrity of these graphs calculated. Also, the domination integrity of the graph E_p^t is obtained. In last section, the domination integrity of some graph products are investigated. Firstly, the domination integrity of graphs B_n xC_m and B_n xP_m are calculated. Then, G_n and G_m are a graphs with order of n and m, the graph of G_n oG_m is investigated and the domination integrity of this graph is calculated.