1 / 20

# Ch. 15: Graph Theory Some practical uses - PowerPoint PPT Presentation

Ch. 15: Graph Theory Some 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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Ch. 15: Graph Theory Some practical uses' - tan

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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 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 problem

B C

D

A A

A B A B C CC

B D

C D D E F B

E

A B

C D

A B C A B A

B C

C D C D D

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:

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)

A

A B C A B

B C

D

D E C D

Hamilton paths and circuits at degrees)

A B A B A B C

C D C D D E F G

E

hw at degrees)