Phasor Measurement Devices (PMU) continuously provides the time-synchronized measurements of a power system by using signals from Global Positioning System (GPS). These accurate measurements help in the field of security, protection and control study of a power system. This paper presents a novel technique to monitor the distribution system by using micro-PMU. Optimal PMU placement problem has been solved by using graph-theoretic approaches. Initially, a given test system is converted to a graph model. Typically, spanning tree contains two types of vertex-pendant vertex and cut vertex. Primarily, some strategic locations have been indicated for PMU placements according to the positions of pendant vertices and cut vertices. Finally, a specific technique has been followed to make the system completely observable. IEEE 13-node, 34-node, and 37-node test feeders have been used to check the efficacy of the proposed technique. The outcome of the proposed technique is compared with some other methods.