A Sufficient Condition for a Graph to be a Fractional $(a,b,n)$-Critical Deleted Graph

Abstract

The toughness, as the parameter for measuring stability and vulnerability of networks, has been widely used in computer communication
networks and ontology graph structure analysis. A graph $G$ is called a fractional $(a,b,n)$-critical deleted graph if after deleting any $n$ vertices from $G$, the resulting graph is still a fractional $(a,b)$-deleted graph. In this paper,we study the relationship between toughness and fractional $(a,b,n)$-critical deleted graph. A sufficient condition for a graph G to be a fractional $(a,b,n)$-critical deleted graph is determined.