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 Ratings
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| Reviewed: |
Jun 02, 2006 by Mathematics |
| Overview: |
This applet is part of a larger collection of lessons on graph theory. The
focus of this particular applet is on Euler Circuits, Directed Graphs and
Hamilton Circuits.
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| Learning Goals: |
Investigate existence of Euler Circuits and Hamilton Circuits for a variety of
graphs. The applet also defines directed graphs and n cubes.
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| Target Student Population: |
Undergraduate graph theory and discrete mathematics courses.
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| Prerequisite Knowledge or Skills: |
Basic terms and definitions in graph theory and the lessons 1-11 given on the
parent site.
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| Type of Material: |
Tutorial & simulation
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| Recommended Uses: |
Classroom demo, student tutorials
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| Technical Requirements: |
JAVA 2 enabled browser, Peterson software
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| Strengths: |
This lesson begins with brief definitions of an Euler circuit and Euler path.
The student is then asked to explore Euler circuits on complete graphs using an
applet. The applet efficiently demonstrates what an Euler circuit is. There
are more questions about which other graphs contain Euler circuits, and the
student is asked to use the Peterson software (see below) to make this
investigation. The lesson is well laid out and the coordinated use of text,
Java, and the Peterson software is handled well. The second part of the lesson,
directed graphs, continues with the theme of text, Java, and the Peterson
software. The third part of the lesson provides a definition of a Hamiltonian
Circuit and explores their existence in the same manner as previously discussed
for the Euler Circuit. Upon completion of the lesson, the user can easily
compare the criteria required for existence of the Euler and Hamilton Circuits
on the specified graphs.
When the author uses a term that was introduced in a previous lesson, he makes
sure to provide a link to the page with its definition. At the bottom of the
page there is a link to the answers for the lesson.
The lessons are well sequenced and include all of the expected topics in
introductory graph theory. Instructions and definitions are clear and followed
by examples for the user to follow, both in the applet and using the Peterson
software. Lessons reinforce concepts defined in earlier lessons, increasing
retention.
The author forwarded an exam copy of the Peterson software for completion of the
review. It was excellent in its instruction, but limited to 16 vertices.
Occasionally a lesson requested use of a larger number of vertices than the
program could accommodate,
but using a smaller number was equally instructive.
The complete version of Peterson software is available from the author for $15
and accommodates 64 vertices.
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| Concerns: |
none
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Potential Effectiveness as a Teaching Tool |
Rating:  |
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| Strengths: |
This applet is part of a large series of lessons that comprehensively address
elementary graph theory. Assuming that the student has worked through lessons
1-11, the student can work on lesson 12 without the aid of the instructor. It
will serve as an excellent supplement to any discussion of Euler circuits,
Hamilton Circuits and directed graphs. Both the applet and the Peterson
software show the Euler circuits and Hamilton Circuits animated through its
graph. The questions encourage exploration and the answers are provided via a
link.
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| Concerns: |
none
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Ease of Use for Both Students and Faculty |
| Rating: |
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| Strengths: |
Drawing the vertices and edges are easy and the user can easily modify a graph
without starting over. The Peterson software has a menu interface and is also
very easy to use. By starting with the simpler Java applet before working on
the Peterson software, the student may create his/her graphs and experiment with
them, gradually learning the concepts without becoming frustrated.
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| Concerns: |
This lesson would be difficult to follow if the student didnt work through the
prior lessons first. This is more of a caution than a concern. On some
screens, the student will need to change the graph size to smaller in order to
fit the whole graph on the screen.
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| Other Issues and Comments: |
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