A mild changed condition for fractional (g,f, n)-critical deleted graph

Abstract

A graph G is fractional (g, f, n)-critical deleted if after deleting any edge e, the resulting graph is still a fractional (g, f, n)-critical graph. In Gao and Wang [8], it is presented that G is a fractional (g, f, n)-critical graph if I(G) ≥ b²+bn-Δ/a, where I(G) is the isolated toughness of graph G. The aim of this work is to reveal that after mild changing of this bound, we obtain an isolated toughness condition for a graph to be fractional (g, f, n)- critical deleted. Furthermore, we show that this conclusion can help to directly deduce an I(G) bound for all fractional (g, f, n)-critical deleted graphs. Finally, we propose an open question for a more generalized case. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.