Toughness condition for a graph to be a fractional (g, f, n)-critical deleted graph

A graph G is called a fractional (g, f)-deleted graph if G - {e} admits a fractional (g, f)-factor for any e ∈ E(G). A graph G is called a fractional (g, f, n)-critical deleted graph if, after deleting any n vertices from G, the resulting graph is still a fractional (g, f)-deleted graph. The toughness, as the parameter for measuring the vulnerability of communication networks, has received significant attention in computer science. In this paper, we present the relationship between toughness and fractional (g, f, n)-critical deleted graphs. It is determined that G is fractional (g, f, n)-critical deleted if t(G) ≥ ((b (2) - 1 + bn)/a).