Computing tenacity, rupture degree and some other vulnerability parameters in polynomial time for classes of intersection graphs

In communication networks, greater degrees of stability or less vulnerability is required. The vulnerability of communication network measures the resistance of the network to the disruption of operation after the failure of certain stations or communications links. Thus communication networks 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. These desirable properties of the networks can be measured by various graph parameters like toughness, integrity, scattering number, tenacity, rupture degree and etc. In general, computing of these parameters is NP-complete or NP-hard, but in this paper we will show that some of these parameters can be computed in polynomial time for classes of intersection graphs such as interval graphs, trapezoid graphs and etc.