Consider a real-world situation that could be modelled with a graph. A reminder that the meaning of graph you are discussing in this unit simply refers to a structure that will model relationships between entities. A graph consists of a discrete number of points (vertices) and the lines that connect them (edges). There are many examples that have been shared in your textbook chapter as well as the course notes. Here are some additional examples:

·         Connecting high speed network cables to all university campus buildings

·         A school bus route picking up all children in their route

·         A rock band planning their yearlong tour route

Initial post: Consider a situation that involves relationships that can be modelled with a graph. It should include between 5–10 vertices and 5–10 edges.

1) In at least one well composed paragraph, describe the context for the situation.

2) What does each vertex represent? How many are there?

3) What does each edge represent? How many are there?

4) Draw a graph using a drawing program of your choice and attach it as a link or attachment. Make sure to label your vertices with a single capital letter (A, B, C, D, E …)

First Response to a Classmate: Review a different classmate’s post. Answer the following questions:

1) In your own words, explain to your classmate the difference between a path and a circuit in a graph. For all references used, please cite them in APA format.

2) Are there any paths or circuits in their post?

3) Are there any paths or circuits in their graph? If so, identify at least one path and circuit.

Second Response to a Classmate: Review a different classmate’s post. Answer the following questions:

1) In your own words, explain to your classmate the difference between an Euler circuit/path and a Hamiltonian path/circuit. This should be at least one well composed paragraph. For all references used, please cite them in APA format.

2) In the context of their situation, could you find an Euler or a Hamiltonian path/circuit for their situation?

3) (OPTIONAL) What is the most efficient route? You can use any of the algorithms that have been learned. Describe in detail the route and how you determined it.

Discussion Requirements

Throughout this course, you will respond to other people’s opinions and comments by participating in the Discussion Boards. It is helpful to complete your Reading prior to answering the Discussion topics.

The complete Discussion topics can be found by clicking on the Discussion content item in the menu to the left under this unit. Be sure to answer one of the provided questions, comment on at least two of your classmates' posts, and engage one another in discussion.

Discussion Board grading rubrics include points for posts which “…contribute to the quality of the discussion.” In order to earn full credit, students are strongly encouraged to post by Saturday night so that posts will engage other students and provide a quality contribution. Be sure your post is grammatically correct, has been spell checked, and you have fully answered the question. A response to a classmates’ post must be substantive; posts such as “Great job” or “I agree” will not be counted as a response. See the rubric for further details. Provide citations for any websites referred to in your posts and summarize in your own words any information shared in your post.

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