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10. POLYHEDRA AND NETWORKS

10. POLYHEDRA AND NETWORKS. Konigsberg Bridge Problem. A. Start on any land mass Cross each bridge once and only once Can you do it?. B. D. C. Introduction to Graph Theory. A graph is any collection of Dots ( Vertices ) Arcs/Lines ( Edges ) that join the points.

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10. POLYHEDRA AND NETWORKS

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  1. 10. POLYHEDRA AND NETWORKS

  2. Konigsberg Bridge Problem A • Start on any land mass • Cross each bridge once and • only once • Can you do it? B D C

  3. Introduction to Graph Theory A graph is any collection of • Dots (Vertices) • Arcs/Lines (Edges) that join the points

  4. Traversability • A network is said to be Traversable if you can draw it without removing your pen from the paper and without retracing the same arc twice. Are these Graphs Traversable?

  5. What is the difference between the 3 graphs? No Yes Yes

  6. To be traversable it must have 2 or 0 odd nodes In order to start and end at the same node the network must be Eularian (all nodes must be even). If exactly two nodes have odd order, the network is still traversable, but you start and end at different nodes (and the network is Semi-Eularian)

  7. Traversability • A network is said to be Traversable if you can draw it without removing your pen from the paper and without retracing the same arc twice. It is Closed if you can start anywhere and finish at the start point. Are these Graphs Traversable? Are they closed? Yes Yes Yes Traversable? No Yes Yes Closed?

  8. For each network, count the number of odd vertices and the number of even vertices, then complete the table.

  9. Matrix of a Graph

  10. THANK YOU

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