—The isolated toughness and binding number, as the parameters for measuring stability and vulnerable of networks, have been widely used in computer communication networks. The concept of fractional critical deleted graph is used to measure whether there exists a feasible data packet transmission scheme from site to site when certain intermediate channels and sites are damaged. In this paper, we study the relationship between fractional critical deleted graph and vulnerability parameters. It is highlighted that a graph G is a fractional critical deleted graph if its isolated toughness or binding number meets certain conditions. Furthermore, some conditions we give in the article is sharp in some sense.
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