Spectrum bounds for the scattering number, integrity, tenacity of regular graphs

There are several measures or graph parameters of the vulnerability and reliability of a communication network, such as connectivity, toughness, scattering number, integrity, tenacity, rupture degree and edge-analogues of some of them. Among these parameters, the scattering number, integrity, tenacity are the better ones to measure the stability of a network. When designing stable networks, it is often required to know the structure of networks attaining the maximum and minimum values of given stability parameters with prescribed number of communications stations and links. In this paper, we present some new bounds for the scattering number, integrity, tenacity of regular graphs in terms of the spectrum.