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Distribution system restoration (DSR) is aimed at restoring loads after a fault by altering the topological structure of the distribution network while meeting electrical and operational constraints. The emerging microgrids embedded in distribution systems enhance the self-healing capability and allow distribution systems to recover faster in the event of an outage. This paper presents a graph-theoretic DSR strategy incorporating microgrids that maximizes the restored load and minimizes the number of switching operations. Spanning tree search algorithms are applied to find the candidate restoration strategies by modeling microgrids as virtual feeders and representing the distribution system as a spanning tree. Unbalanced three-phase power flow is performed to ensure that the proposed system topology satisfies all operational constraints. Simulation results based on a modified IEEE 37-node system and a 1069-node …