Abstract
Let i >= 2, Delta >= 0, 1 <= a <= b - Delta, n > (a+b)(ib+2m-2)/a + n' and delta(G) >= b(2)/a n' + 2m, and let g, f be two integer-valued functions defined on V(G) such that a <= g(x) <= f(x) - Delta <= b - Delta for each x is an element of V(G). In this article, it is determined that G is a fractional (g, f, n', m)-critical deleted graph if max{d(1), d(2), ... , d(i)) >= b(n+n')/a+b for any independent subset {x(1), x(2), ... , x(i)} subset of V(G). The result is tight on independent set degree condition.