Toughness Condition for a Graph to Be a Fractional(g,f,n)-Critical Deleted Graph

Abstract

A graphGis called a fractional(g,f)-deleted graph ifG-{e}admits a fractional(g,f)-factor for anye∈E(G). A graphGis called a fractional(g,f,n)-critical deleted graph if, after deleting anynvertices fromG, 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 thatGis fractional(g,f,n)-critical deleted ift(G)≥((b2-1+bn)/a).