Ch 15 graph theory some practical uses
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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

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Ch 15 graph theory some practical uses
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 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

Konigsberg bridge problem


A

B C

D


Are there euler paths or circuits for these graphs
Are there Euler paths or circuits for these graphs?

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


Q when is there an euler circuit or path
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
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
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
Hamilton paths and circuits at degrees)

A

A B C A B

B C

D

D E C D


Hamilton paths and circuits1
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)


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