Abstract
A graph
G
is called a fractional (
g
,
f
,
m
)-deleted graph if the resulting graph admits a fractional (
g
,
f
)-factor after
m
edges are removed. An important fact in the characterization of a discrete graph dynamical system is played by the independent sets, i.e., subsets of the vertex set of
G
in which any two of them are not adjacent because they reflect the sparsity and stability of the graph system in somehow. The neighborhoods union of independent sets characterizes the local density and local clustering characteristics of the graph system. In this paper, we study the relationship between characteristics of independent sets and fractional (
g
,
f
,
m
)-deleted graph systems. The main contributions cover two aspects: first, we present an independent set degree condition for a graph to be fractional (
g
,
f
,
m
)-deleted; later an independent set neighborhood union condition for fractional (
g
,
f
,
m
)-deleted graphs is determined. Furthermore, we show that the results obtained are the best in some sense.