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power point for contemporary math ch 6

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A Mathematical View of Our World 1 st ed. Parks, Musser, Trimpe, Maurer, and Maurer
Chapter 6 Routes and Networks
Section 6.1 Routing Problems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
6.1 Initial Problem ,[object Object],[object Object]
Graphs ,[object Object],[object Object]
Graphs ,[object Object],[object Object],[object Object]
Equivalent Graphs ,[object Object]
Example 1 ,[object Object],A is connected to B, B to C, and C to D
Vertices and Edges ,[object Object],[object Object]
Example 2 ,[object Object],[object Object]
Example 2 ,[object Object],[object Object]
Example 3 ,[object Object],[object Object]
Example 3, cont’d ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example 4 ,[object Object],[object Object],[object Object],[object Object]
Example 4, cont’d ,[object Object],[object Object],[object Object],[object Object]
Degree of a Vertex ,[object Object],[object Object],[object Object]
Example 5 ,[object Object]
Example 5 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example 5 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Theorem ,[object Object],[object Object],[object Object]
Example 6 ,[object Object],[object Object]
Paths ,[object Object],[object Object],[object Object],[object Object]
Example 7 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Circuits ,[object Object],[object Object]
Euler Paths ,[object Object],[object Object]
Euler Circuits ,[object Object],[object Object]
Connected Graphs ,[object Object],[object Object],[object Object]
Example 8 ,[object Object],[object Object]
Example 8, cont’d ,[object Object]
Example 9 ,[object Object],[object Object]
Example 10 ,[object Object],[object Object]
Degree Theorem ,[object Object],[object Object],[object Object],[object Object]
Euler’s Theorem ,[object Object],[object Object],[object Object]
Euler’s Theorem cont’d ,[object Object],[object Object],[object Object],[object Object],[object Object]
Euler’s Theorem cont’d ,[object Object],[object Object],[object Object],[object Object]
Example 11 ,[object Object],2 F 2 E 4 D 2 C 4 B 4 A Degree Vertex
Example 11 ,[object Object],[object Object]
Example 11, cont’d ,[object Object]
Fleury’s Algorithm ,[object Object],[object Object],[object Object],[object Object]
Fleury’s Algorithm, cont’d ,[object Object],[object Object],[object Object]
Fleury’s Algorithm, cont’d ,[object Object],[object Object]
Example 12 ,[object Object],[object Object]
6.1 Initial Problem Solution ,[object Object]
Initial Problem Solution, cont’d ,[object Object],[object Object]
Section 6.1 Assignment ,[object Object]
Section 6.2 Network Problems ,[object Object],[object Object],[object Object],[object Object],[object Object]
6.2 Initial Problem ,[object Object],[object Object],[object Object],[object Object]
Weighted Graphs ,[object Object]
Example 1 ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example 1, cont’d ,[object Object],[object Object],[object Object],[object Object]
Example 1, cont’d ,[object Object]
Redundant Edges ,[object Object],[object Object],[object Object]
Subgraphs ,[object Object],[object Object]
Subgraphs ,[object Object]
Example 2 ,[object Object],[object Object],[object Object]
Example 2 ,[object Object]
Example 2 ,[object Object]
Example 2 ,[object Object]
Trees ,[object Object],[object Object],[object Object]
Trees, cont’d ,[object Object]
Example 3 ,[object Object],[object Object]
Example 3 ,[object Object]
Spanning Trees ,[object Object],[object Object],[object Object],[object Object]
Spanning Trees ,[object Object],[object Object]
Minimal Spanning Trees ,[object Object],[object Object]
Minimal Spanning Trees ,[object Object],[object Object],[object Object]
Kruskal’s Algorithm ,[object Object],[object Object]
Kruskal’s Algorithm ,[object Object],[object Object]
Kruskal’s Algorithm ,[object Object],[object Object]
Kruskal’s Algorithm ,[object Object],[object Object]
Kruskal’s Algorithm ,[object Object],[object Object]
Kruskal’s Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Example 4 ,[object Object]
Example 4 ,[object Object],[object Object],[object Object]
Example 4 ,[object Object],[object Object],[object Object]
Example 4 ,[object Object],[object Object],[object Object]
Example 4 ,[object Object],[object Object],[object Object]
6.2 Initial Problem Solution ,[object Object]
Initial Problem Solution ,[object Object],[object Object]
Initial Problem Solution ,[object Object],[object Object]
Initial Problem Solution ,[object Object],[object Object]
Section 6.2 Assignment ,[object Object]
Section 6.3 Traveling-Salesperson Problem ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
6.3 Initial Problem ,[object Object],[object Object]
Hamiltonian Circuits ,[object Object],[object Object]
Example 1 ,[object Object],[object Object]
Example 2 ,[object Object],[object Object]
Hamiltonian Circuits, cont’d ,[object Object],[object Object]
Example 3 ,[object Object]
Example 3 ,[object Object],[object Object],[object Object]
Example 3, cont’d ,[object Object],[object Object]
Example 3, cont’d ,[object Object],[object Object],[object Object],[object Object]
Complete Graphs ,[object Object]
Example 4 ,[object Object]
Example 4, cont’d ,[object Object],[object Object]
Example 4, cont’d ,[object Object],[object Object]
Example 4, cont’d ,[object Object],[object Object]
Complete Graphs ,[object Object],[object Object],[object Object],[object Object]
Example 6 ,[object Object]
Example 6, cont’d ,[object Object]
Example 6, cont’d ,[object Object],[object Object],[object Object]
Theorem on Complete Graphs ,[object Object],[object Object],[object Object]
Question: ,[object Object],[object Object],[object Object],[object Object],[object Object]
Question: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Traveling-Salesperson Problem ,[object Object],[object Object]
Complete Weighted Graphs ,[object Object],[object Object]
Question: ,[object Object],[object Object],[object Object],[object Object],[object Object]
Question: ,[object Object],[object Object],[object Object],[object Object],[object Object]
Example 7 ,[object Object],[object Object]
Example 7, cont’d ,[object Object],[object Object]
Example 7, cont’d
Example 7, cont’d ,[object Object],[object Object],[object Object]
Example 7, cont’d ,[object Object],[object Object]
Example 7, cont’d ,[object Object]
Example 7, cont’d ,[object Object],[object Object],[object Object],[object Object]
Traveling-Salesperson, cont’d ,[object Object],[object Object],[object Object],[object Object],[object Object]
Traveling-Salesperson, cont’d ,[object Object],[object Object],[object Object],[object Object],[object Object]
6.3 Initial Problem Solution ,[object Object]
Initial Problem Solution, cont’d ,[object Object],[object Object],[object Object]
Initial Problem Solution, cont’d ,[object Object],[object Object],[object Object]
Initial Problem Solution, cont’d ,[object Object],[object Object]
Initial Problem Solution, cont’d ,[object Object],[object Object]
Initial Problem Solution, cont’d ,[object Object],[object Object]
A fun website with Traveling Salesman Problem (TSP) Artwork: http://www.oberlin.edu/math/faculty/bosch/tspart-page.html
Section 6.3 Assignment ,[object Object]
Chapter 6 Assignments ,[object Object],[object Object],[object Object]

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nossi ch 6

  • 1. A Mathematical View of Our World 1 st ed. Parks, Musser, Trimpe, Maurer, and Maurer
  • 2. Chapter 6 Routes and Networks
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  • 124. A fun website with Traveling Salesman Problem (TSP) Artwork: http://www.oberlin.edu/math/faculty/bosch/tspart-page.html
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