1 / 18

Topological Graph Theory

David Craft. Topological Graph Theory. Mathematics Combinatorics Graph Theory Topological Graph Theory. A graph is a set of vertices (or points). A graph is a set of vertices (or points). together with a set of vertex-pairs called edges . .

nami
Download Presentation

Topological Graph Theory

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. David Craft Topological Graph Theory Mathematics Combinatorics Graph Theory Topological Graph Theory

  2. A graphis a set of vertices(or points)

  3. A graph is a set of vertices (or points) together with a set of vertex-pairs called edges.

  4. A graph is a set of vertices (or points) A graph is a set of vertices (or points) together with a set of vertex-pairs called edges. together with a set of vertex-pairs called edges. Graph Theory is the study of graphs.

  5. An imbeddingor embedding (or properdrawing) of a graph is one in which edges do not cross.

  6. An imbedding or embedding (or properdrawing) of a graph is one in which edges do not cross. NOT an imbedding

  7. An imbedding or embedding (or properdrawing) of a graph is one in which edges do not cross. NOT an imbedding An imbedding

  8. An imbedding or embedding (or properdrawing) of a graph is one in which edges do not cross. NOT an imbedding An imbedding Topological Graph Theory is the studyof imbeddings of graphs in various surfaces or spaces

  9. Orientable surfaces (without boundary): sphere S0

  10. Orientable surfaces (without boundary): Orientable surfaces (without boundary): sphere S0 sphere S0 torus S1 torus S1

  11. Orientable surfaces (without boundary): Orientable surfaces (without boundary): sphere S0 sphere S0 torus S1 torus S1 2-torus S2 2-torus S2

  12. Orientable surfaces (without boundary): Orientable surfaces (without boundary): sphere S0 sphere S0 torus S1 torus S1 2-torus S2 2-torus S2 n-torus Sn n-torus Sn

  13. Orientable surfaces (without boundary): sphere S0 torus S1 2-torus S2 The surface Sn is said to have genus n n-torus Sn

  14. Some graphs cannot be imbedded in the sphere… ? ? ?

  15. Some graphs cannot be imbedded in the sphere… ? ? …but all can be imbedded in in a surface of high enough genus.

  16. The main problem in topological graph theory: Given a graph G, determine the smallest genus n so that G imbeds in Sn.

  17. The main problem in topological graph theory: Given a graph G, determine the smallest genus n so that G imbeds in Sn. For G = the answer is n = 1.

  18. The main problem in topological graph theory: Given a graph G, determine the smallest genus n so that G imbeds in Sn. For G = the answer is n = 1. For G = the answer is n = 3.

More Related