Fault diagnosis is an important task for the safe and optimal operation of chemical processes. Hence, this area has attracted considerable attention from researchers in the past few years. A variety of approaches have been proposed for solving this problem. All approaches for fault detection and diagnosis in some sense involve the comparison of the observed behavior of the process to a reference model. The process behavior is inferred using sensors measuring the important variables in the process. Hence, the efficiency of the diagnostic approach depends critically on the location of sensors monitoring the process variables. The emphasis of most of the work on fault diagnosis has been more on procedures to perform diagnosis given a set of sensors and less on the actual location of sensors for efficient identification of faults. A digraph-based approach is proposed for the problem of sensor location for identification of faults. Various graph algorithms that use the developed digraph in deciding the location of sensors based on the concepts of observability and resolution are discussed. Simple examples are provided to explain the algorithms, and a complex FCCU case study is also discussed to underscore the utility of the algorithm for large flow sheets. The significance and scope of the proposed algorithms are highlighted.