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Lecture 16: Graph Theory III

Lecture 16: Graph Theory III. Discrete Mathematical Structures: Theory and Applications. Learning Objectives. Learn the basic properties of graph theory Learn about walks, trails, paths, circuits, and cycles in a graph Explore how graphs are represented in computer memory

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Lecture 16: Graph Theory III

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  1. Lecture 16: Graph Theory III Discrete Mathematical Structures: Theory and Applications

  2. Learning Objectives • Learn the basic properties of graph theory • Learn about walks, trails, paths, circuits, and cycles in a graph • Explore how graphs are represented in computer memory • Learn about Euler and Hamilton circuits • Explore various graph algorithms • Examine planar graphs and graph coloring Discrete Mathematical Structures: Theory and Applications

  3. Graph Algorithms • Graphs can be used to show how different chemicals are related or to show airline routes. They can also be used to show the highway structure of a city, state, or country. • The edges connecting two vertices can be assigned a nonnegative real number, called the weight of the edge. • If the graph represents a highway structure, the weight can represent the distance between two places, or the travel time from one place to another. • Such graphs are called weighted graphs. Discrete Mathematical Structures: Theory and Applications

  4. Graph Algorithms Discrete Mathematical Structures: Theory and Applications

  5. Graph Algorithms Discrete Mathematical Structures: Theory and Applications

  6. Graph Algorithms Discrete Mathematical Structures: Theory and Applications

  7. Graph Algorithms Discrete Mathematical Structures: Theory and Applications

  8. Discrete Mathematical Structures: Theory and Applications

  9. 2 1 2 3 4 5 6 7 3 1 3 9 5 2 0 3 1 10 4 2 2 From 1 to 6 8 4 5 6 1 8 6 Discrete Mathematical Structures: Theory and Applications

  10. Graph Algorithms Discrete Mathematical Structures: Theory and Applications

  11. Planar Graphs and Graph Coloring Discrete Mathematical Structures: Theory and Applications

  12. Planar Graphs and Graph Coloring • A graph is a planar graph if and only if it has a pictorial representation in a plane which is a plane graph. This pictorial representation of a planar graph G as a plane graph is called a planar representation of G. • Let G denote the plane graph in Figure 10.111. Graph G, in Figure 10.111, divides the plane into different regions, called the faces of G. Discrete Mathematical Structures: Theory and Applications

  13. Planar Graphs and Graph Coloring Discrete Mathematical Structures: Theory and Applications

  14. Planar Graphs and Graph Coloring Discrete Mathematical Structures: Theory and Applications

  15. Planar Graphs and Graph Coloring Discrete Mathematical Structures: Theory and Applications

  16. Planar Graphs and Graph Coloring Discrete Mathematical Structures: Theory and Applications

  17. Planar Graphs and Graph Coloring Discrete Mathematical Structures: Theory and Applications

  18. Discrete Mathematical Structures: Theory and Applications

  19. Discrete Mathematical Structures: Theory and Applications

  20. Planar Graphs and Graph Coloring Discrete Mathematical Structures: Theory and Applications

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