Secure operating conditions must be maintained under different events. This paper proposes the creation of islands as a strategy that consists of tripping off properly selected lines in order to separate the power network into islands as a way to improve the security of the power system. In the last decade, several collapses have occurred around the world. This defensive strategy would allow safeguarding the power system when cascading failures spread rapidly through of the interconnected network. The strategy proposed in this paper is based on Spectral Graph Theory. Graph eigenvalue analysis provides some insight into the intrinsic structure of the power systems. The concepts are illustrated by splitting of the 68-bus test systems into islands. Finally, the paper offers a dynamic analysis of the 68-bus test system to demonstrate how the splitting strategy would work.