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This paper deals with distribution network (DN) reconfiguration for loss minimization. To solve this combinatorial problem, a genetic algorithm (GA) is considered. In order to enhance its ability to explore the solution space, efficient genetic operators are developed. After a survey of the existing DN topology description methods, a theoretical approach based on the graph and matroid theories (graphic matroid in particular) is considered. These concepts are used in order to propose new intelligent and effective GA operators for efficient mutation and crossover well dedicated to the DN reconfiguration problem. All resulting individuals after GA operators are claimed to be feasible (radial) configurations. Moreover, the presented approach is valid for planar or nonplanar DN graph topologies and avoids tedious mesh checks for the topology constraint validation. The proposed method is finally compared to some previous topology coding techniques used by other authors. The results show smaller or at least equal power losses with considerably less computation effort.