| Vertex-Edge
Graphs |
• Explanation of the fact that only four colors are needed to color a map or picture
with different sections
• Definition of Edge and Vertex
• The use of odd and even vertices to determine whether only 2 colors are needed
or if 3 or 4 colors are required
• Interactive practice coloring complex figures in a strategic manner
• Review and continuation of methods for coloring complex figures
• Edge verses Perimeter
• Review and continuation of methods for coloring complex figures
• The importance of Edges separating conflicting color areas in a picture or map
• Creation of a Vertex-Edge Graph from a color picture.
• Creation of a Vertex-Edge Graph from a map
• Definition and examples of a Path on a Vertex-Edge Graph; interactive practice
• Weights (time and distance) on the Edges of a Vertex-Edge graph;
interactive practice
• Definition and examples of a Circuit on a Vertex-Edge graph
• Review and continuation of methods for coloring complex figures
• The importance of Edges separating conflicting color areas in a picture or map
• Creation of a Vertex-Edge Graph from a color picture.
• Creation of a Vertex-Edge Graph from a map
• Definition and examples of a Path on a Vertex-Edge Graph; interactive practice
• Weights (time and distance) on the Edges of a Vertex-Edge graph; interactive practice
• Definition and examples of a Circuit on a Vertex-Edge graph
• Definition of an Euler Path and Circuit; interactive practice
Lesson
Homework
User Instructions
Note: Lesson file is very large and may take a few minutes to download depending on your connect speed.
Homework
User Instructions
Note: Lesson file is very large and may take a few minutes to download depending on your connect speed.
• Review of the derivation of a Vertex-Edge Graph from a picture, emphasizing the role of Edges.
• Conflict Resolution using Vertex-Edge Graphs; interactive practice:
○ After School Activities
–
determining the minimum number of meeting times for
all
students to attend all their desired extracurricular
activities
○ Habitat Problem – The minimum number of habitats needed to house 8 animals some of which cannot live in the same habitat.
○ Bat Project– The minimum number of days needed so that students can meet in two groups, each studying a particular type of bat.
○ Movies - The number of visits to the movie theater so all 5 students can each see their two favorite movie.
○ Habitat Problem – The minimum number of habitats needed to house 8 animals some of which cannot live in the same habitat.
○ Bat Project– The minimum number of days needed so that students can meet in two groups, each studying a particular type of bat.
○ Movies - The number of visits to the movie theater so all 5 students can each see their two favorite movie.
Download
Description
of
Lesson
• Creation of a Vertex-Edge Graph from a color picture or map.
• Definition and examples of Paths and Circuits on a Vertex-Edge Graph
• Weights (time and distance) on the Edges of a Vertex-Edge graph
• Definition of Euler Paths and Euler Circuits
• Interactive practice problems
• Creation of a Vertex-Edge Graph from a color picture or map.
• Definition and examples of Paths and Circuits on a Vertex-Edge Graph
• Weights (time and distance) on the Edges of a Vertex-Edge graph
• Definition of Euler Paths and Euler Circuits
• Interactive practice problems
• Review of Euler Paths and Euler Circuits
• The Degree of a Vertex
• The rules for determining Euler Paths and Circuits
• Interactive problem solving using Euler Paths and Circuits
Download
Description
of Lesson
• The rules for determining Hamilton Paths and Circuits
• Interactive problem solving using Hamilton Paths and Circuits
• Solving shortest route problems
• The rules for determining Hamilton Paths and Circuits
• Interactive problem solving using Hamilton Paths and Circuits
• Solving shortest route problems