Most of the networks are generally less energy efficient and most of the time re-sources are underutilized. Even resources of busy networks are also underutilized and thus networks show energy inefficient management system. This paper focuses on how to obtain minimum resources for the current situation of the network to maintain connectivity, power saving and quality of service. Four different models are proposed in this perspective with different purposes and functions. These mod-els determine the minimum resources under certain constrains. Two types of services namely, minimum bandwidth and trivial file transfer are considered. For minimum bandwidth service, minimum edge, mini-mum delay and minimum change models are proposed. Here data rate switch and enable/disable of edges are placed in these models for power saving strategy. Another model, multi flow is proposed for trivial file transferservice. It is proposed for transferring files through multiple flows in multiple paths from source to destination. All models except multi flow model are mixed integer programming optimization problem.