Initial post + 2 responses to classmates (see attached)

Graphs for Modeling Real-World Situations

Post 1: Initial Response

Imagine a real-world situation that involves relationships that can be modeled with a graph. A graph consists of a discrete number of vertices and the edges that connect them. When brainstorming the situation you would like to model with a graph, review the examples that have been presented in your unit readings and homework exercises for ideas.

1. Consider a situation in your personal or professional world that involves relationships that can be modeled with a graph. Describe this situation in at least one well-composed paragraph, sharing:
   • A brief description of the situation modeled,
   • What each vertex represents, and
   • What each edge represents.
2. Draw a connected graph using a drawing program of your choice and include it in your post. The following must be present in your graph:
   • 5–10 vertices, each clearly labeled with a single capital letter (A, B, C, D, E …)
   • At least 2 vertices of degree 3 or more (the degree of a vertex is the count of how many edges are attached to that vertex).
   • At least 1 circuit.

View Unit 7 Discussion Post 1 example.

Post 2: Reply to a Classmate
Review a classmate's post and consider their real-world context. Address all of the following items. For all references used, please cite them in APA format. No explanations may be taken directly word for word from another source.

1. In your own words, explain to your classmate what is required for a trail or circuit to be a Euler trail or circuit.
2. Does a Euler trail exist for their graph? Explain specifically using the label and degree of each vertex.
3. Does a Euler circuit exist for their graph? Explain specifically using the label and degree of each vertex.

View Unit 7 Discussion Post 2 example.

Post 3: Reply to Another Classmate

Review a different classmate's post and consider their real-world context. Address all of the following items. For all references used, please cite them in APA format. No explanations may be taken directly word for word from another source.

1. In your own words, explain to your classmate what is required for a walk to be a Hamiltonian path or cycle.
2. Identify one sequence of vertices that makes either a Hamiltonian path or a Hamiltonian cycle.
3. Based on the context of your classmate's situation modeled by the graph, think about whether it would be most practical to seek a Euler trail or circuit versus a Hamiltonian path or cycle. Which one do you think would be more useful in your classmate's situation and why?