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Weighted Graph mmw - Review

Review
Course

Bachelor of Science in Information Technology (BSIT)

933 Documents
Students shared 933 documents in this course
Academic year: 2022/2023
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Polytechnic University of the Philippines

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WEIGHTED GRAPH

A weighted graph is a graph in which each edge is associated with a value, called a weight. The value can represent any quantity we desire A route that visits each city just once corresponds to a Hamiltonian circuit. a. Chicago – New York – Dallas

  • Philadelphia – Atlanta – Washington, D. – Chicago 713 + 1374 + 1299 + 670 + 544 + 597 = 5197 b. Chicago – Philadelphia – Dallas – Washington, D. – Atlanta – New York – Chicago 665 + 1299 + 1185 + 544 + 748 + 713 = 5154 c. Chicago – Washington, D. – Dallas – New York – Atlanta – Philadelphia – Chicago 597 + 1185 + 1374 + 748 + 670 + 665 = 5239

GRAPH COLORING

In the mid-1800s, Francis Guthrie was trying to color a map of the counties of England. So that it would be easy to distinguish the counties, he wanted counties sharing a common border to have different colors. After several attempts, he noticed that four colors were required to color the map, but not more. This observation became known as the four-color problem. Note that the map has only four colors and that no two states that share a common border have the same color.

PLANAR GRAPH

-a graph that can be drawn so that no edge intersects each other (except at vertices) PLANAR NON PLANAR

CHROMATIC NUMBER OF A GRAPH

minimum number of colors needed to color a graph so that no edge connects vertices of the same color Two Colorable Graph Theorem

  • a graph is two colorable if and only if it has no circuits that consist of an odd number of vertices Four-Color Theorem
  • The chromatic number of a planar graph is at most 4
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Weighted Graph mmw - Review

Course: Bachelor of Science in Information Technology (BSIT)

933 Documents
Students shared 933 documents in this course

University: Polytechnic University of the Philippines

Was this document helpful?
WEIGHTED GRAPH
A weighted graph is a graph in which
each edge is associated with a value,
called a weight.
The value can represent any quantity
we desire
A route that visits each city just
once corresponds to a
Hamiltonian circuit.
a. Chicago – New York – Dallas
– Philadelphia – Atlanta –
Washington, D.C. – Chicago
713 + 1374 + 1299 + 670 + 544 +
597 = 5197
b. Chicago – Philadelphia – Dallas – Washington, D.C. – Atlanta –
New York – Chicago
665 + 1299 + 1185 + 544 + 748 + 713 = 5154
c. Chicago – Washington, D.C. – Dallas – New York – Atlanta –
Philadelphia – Chicago
597 + 1185 + 1374 + 748 + 670 + 665 = 5239
GRAPH COLORING
In the mid-1800s, Francis Guthrie was
trying to color a map of the counties of
England. So that it would be easy to
distinguish the counties, he wanted
counties sharing a common border to
have different colors.
After several attempts, he noticed that
four colors were required to color the
map, but not more. This observation
became known as the four-color problem.
Note that the map has only four colors and that no two states that
share a common border have the same color.
PLANAR GRAPH
-a graph that can be drawn so that
no edge intersects each other
(except at vertices)
PLANAR NON PLANAR
CHROMATIC NUMBER OF A GRAPH
minimum number of colors needed to color a
graph so that no edge connects vertices of
the same color
Two Colorable Graph Theorem
- a graph is two colorable if and
only if it has no circuits that
consist of an odd number of
vertices
Four-Color Theorem
- The chromatic number of a planar
graph is at most 4

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