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.

- 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.

- 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.

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

- In your own words, explain to your classmate what is required for a walk to be a Hamiltonian path or cycle.
- Identify one sequence of vertices that makes either a Hamiltonian path or a Hamiltonian cycle.
- 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?