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Ch. 15: Graph Theory Some practical usesPowerPoint Presentation

Ch. 15: Graph Theory Some practical uses

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Ch. 15: Graph TheorySome practical uses

- Degree of separation- Hollywood, acquaintance, collaboration
- Travel between cities
- Konigsberg bridge
- Shortest path
- Least cost
- Schedule exams, assign channels, rooms
- Number of colors on a map
- Highway inspecting, snow removal, street sweeping
- Mail delivery
- Niche overlap- ecology
- Influence graphs
- Round-robin tournaments
- Precedence graphs

See book and written handouts on Graph Coloring, mailroute, and Konigsberg bridge

Euler paths and circuits- definitions

- Euler circuit – a simple circuit containing every edge of G
Note: circuits start and end at the same point

- Euler path – a simple path containing every edge of G
Practical applications of Euler circuits:

Konigsberg bridge

Konigsberg bridge problem

Q—When is there an Euler circuit or path?

A connected multigraph has an Euler circuit iff each of its vertices has _______.

A connected multigraph has an Euler path but not an Euler circuit iff it has exactly _____.

Hamilton circuits and paths at degrees)

- Just touch every vertex once and only once
- We are not concerned with traveling along each edge
- Practical applications of Hamilton paths and circuits:

Do these graphs have Hamilton paths or circuits? at degrees)

A

A B A B C A C

C B D

C D D E F B

E

A B

C D

Hamilton paths and circuits at degrees)

Hamilton paths and circuits at degrees)

Traveling salesman- p. at degrees)845

hw at degrees)

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