Switched systems find wide applications in power systems and power electronics, automotive control, aircraft and air traffic control, network and congestion control, etc. It is well-known that a switched system does not necessarily inherit qualitative properties of its constituent subsystems. Consequently, characterization of stabilizing switching signals constitutes a key topic in the literature. In this talk I will describe a class of algorithms for constructing switching signals that ensure stability of switched systems. The results employ Lyapunov stability theory and graph theoretic tools.