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.