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Graph Theory. ----Konigsberg 7 Bridge Problem. Konigsberg Bridge.

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Graph Theory


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    1. Graph Theory ----Konigsberg 7 Bridge Problem

    2. Konigsberg Bridge • The old Prussian city of Konigsberg was located on the banks of the Pregel River. Part of the city was on two islands that were joined to the banks and each other by seven bridges. The townspeople liked to take walks, or Spaziergangen, about the town across the bridges. Several people apparently bothered by the fact no one could figure out a walk that crossed each bridge just once, for they brought this problem to the attention of the famous mathematician Leonhard Euler. He solved the Spaziergangen problem, thereby giving birth to graph theory and immortalizing the seven Bridge of Konigsberg in mathematics text.

    3. Can you take a walk through the town crossing over every bridge once, and only once? • Image credit :Michael Taylor from simonkneebone.com

    4. Find a cycle in the graph that includes all vertices and edges (such a cycle is called an Euler cycle).---Any edge is not repeated and every vertex is visited at least once.