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Graph Theory

Graph Theory. Introducton. Graph Theory. T. Serino. Vertex: A point. An intersection of two lines (edges). Edge: A line (or curve) connecting two vertices. Loop: An edge that connects a vertex to itself only. Graph Theory. T. Serino.

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Graph Theory

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  1. Graph Theory Introducton

  2. Graph Theory T. Serino Vertex: A point. An intersection of two lines (edges). Edge: A line (or curve) connecting two vertices. Loop: An edge that connects a vertex to itself only.

  3. Graph Theory T. Serino Ex) Represent the "Konigsberg Bridge“ problem using a vertex-edge graph. A A B C B C D D * Vertices represent locations. * Edges represent “connections” between those locations.

  4. Graph Theory T. Serino Ex) Represent this map using a vertex-edge graph. Hint: On map problems, place vertices relative to their actual locations on the map. W K C U O N * Edges represent borders in a map problem.

  5. Graph Theory T. Serino Ex) Represent a floor plan using a vertex-edge graph. C F H P J M Outside O

  6. Graph Theory T. Serino The degreeof a vertex is the number of edges "entering" the vertex. Degree 2 1 2 Degree 3 2 3 Degree 4 2 3 1 1 4

  7. Graph Theory T. Serino Odd and Even vertices If the degree of a vertex is an odd number, then the vertex is considered an odd vertex. If the degree of the vertex is an even number, then the vertex is considered an even vertex.

  8. Graph Theory T. Serino Ex)How many odd vertices are there in this graph? Degree 4 2 odd vertices Degree 4 Degree 0 F Degree 1 Degree 4 Degree 3

  9. Graph Theory T. Serino A path is a sequence of adjacent vertices and the edges connecting them. Given the graph to the left, some examples of paths could be: ABC BCDD CDBCA

  10. Graph Theory T. Serino A circuit is a path that begins and ends at the same vertex. Given the graph to the left, some examples of circuits could be: ABCA CDDBAC

  11. Graph Theory T. Serino On a connected graph, you can draw a path from one vertex to any other vertex.

  12. Graph Theory T. Serino If a graph is not connected, it is disconnected.

  13. Graph Theory T. Serino A bridge is an edge that if removed from a connected graph would create a disconnected graph.

  14. Graph Theory T. Serino

  15. M athematical D ecision M aking

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