Feasibility of data transmission under attack: from isolated toughness variant perspective

The graph model is an appreciable tool for data transmission network, where the feasibility of data transmission in site attack circumstances can be described by fractional critical graphs, and the vulnerability of networks can be measured by isolation toughness variant. This paper considers both the stability of the network and the feasibility of data transmission when the sites are destroyed, and determines the isolated toughness variant bound for fractional $(a,b,n)$-critical graphs, where the parameter n represents the number of damaged sites at a certain moment. A counterexample proves the sharpness of the given isolated toughness variant bound. The main theoretical conclusion provides an equilibrium between performance and cost in network topology designing.