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The graphs appear in many applications such as computer networks, data networks, and PERT networks, when the network includes a small number of devices, it can be drawn easily by hand, as the number of devices increases, drawing becomes a very difficult task. For this problem we will develop a new method for automatic graph drawing based on two steps, the first is applying the topology –shape –metric that is approaching to orthogonal drawings for the grid and the second step is applying the fuzzy genetic algorithm that is directed, in the topology –shape –metric the final drawing is achieved through three sequential steps: planarization, orthogonalization, and compaction. Each of these steps is responsible for the quality of the final drawing. Then the genetic algorithm applied at the planarization step of the topology-shape-metric to find the geometric position of each vertex to minimize bending in the graph. The developed technique generates a greater number of planar embedding by varying the order of edges’ insertion. This is achieved clearly in the Results given in the paper.

Applying Topology-Shape-Metric and FUZZY Genetic Algorithm for Automatic Planar Hierarchical and Orthogonal Graphs