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# Peer Review

## Ratings

### Overall Rating:

Content Quality:
Effectiveness:
Ease of Use:
 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. Learning Goals: Investigate existence of Euler Circuits and Hamilton Circuits for a variety of graphs. The applet also defines directed graphs and n cubes. Target Student Population: Undergraduate graph theory and discrete mathematics courses. Prerequisite Knowledge or Skills: Basic terms and definitions in graph theory and the lessons 1-11 given on the parent site. Type of Material: Tutorial & simulation Recommended Uses: Classroom demo, student tutorials Technical Requirements: JAVA 2 enabled browser, Peterson software

### Content Quality

Rating:
 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. Concerns: none

### Potential Effectiveness as a Teaching Tool

Rating:
 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. Concerns: none

### Ease of Use for Both Students and Faculty

Rating:
 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. Concerns: This lesson would be difficult to follow if the student didnt 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.