Emerging of embedded sensors like cameras, microphone, accelerometers etc, made the emergence of participatory sensing applications. The participator sensors are applied where there is use of users and group of users. The adversary is used to collect and analyses participators location and trajectory data, from which privacy of the system is harmed. By focusing on trajectory privacy, trajectory privacy preserving framework TrPF is proposed. Based on this a theoretical mix zone model with time as a factor from the graph theory is proposed, from which loss of information is less and hence it is cost effective, privacy is protected.