Before revision:  A framework based on swap operations for resolving this problem is presented and two concrete update algorithms based on one-swappable vertices and two-swappble vertex pairs are designed. Both algorithms can compute high-quality independent sets over dynamic graphs with O(\Delta^3) time for general graphs and with O( 1 ) time for bounded-degree graphs.
After revision:  We implement a dynamic (\frac{\Delta 1 ) time for bounded-degree graphs.