For the graceful transition from the analog to digital TV systems, a systematic frequency assignment scheme must be incorporated into the transition planning procedure. In this study, we have studied the frequency assignment methodology for the efficient management of the limited spectrum resources. By applying the graph-theoretic approach, this study developed a new solution method for additional frequency assignment problem whose objective is to assign available frequencies for newly generated requirements (digital TV stations) with minimum reassignment of the preassigned frequencies to LPTV stations while meeting the interference-related constraints. The proposed algorithm can be effectively applied not only to the current digital TV introduction phase but also to the development phase with some further development. This study can be utilized as the basis for the future study on frequency assignments that aims at graceful transition from analog TV to digital TV.