When emergency controls cannot keep the stability of the whole system, it is a critical and efficient way to split the whole system into several small isolated islands. Moreover, the generators in the same island are synchronous. In this work, a mixed integer linear programming (MILP) model is set up to analyze the splitting strategies for power system islanding operations with the objective of minimizing total load shedding. Furthermore, graph theory is employed to transform the splitting strategy into a partition problem, which gives the splitting constraints for a given number of islands. In addition, the budget set is introduced to control the size of each island, which gives a more practical strategy. Finally, IEEE 30-bus, 118-bus, and 300-bus test systems with given groups of asynchronous generators are studied. The results show that a global optimal solution can quickly be achieved by using the MILP model and the branch-and-bound method.