1) Consider a situation in your personal or professional world that involves relationships that can be modelled 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 graph using a drawing program of your choice and include it in your post. The following must be present in your graph:

Five to ten vertices, each clearly labeled with a single capital letter (A, B, C, D, E ...)

At least two 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 one circuit.

Be a connected graph.

3) Consider your graph with the perspective of a Euler path or circuit and explain the following:

In your own words, explain what is required for a path or circuit to be an Euler path or circuit.

Does an Euler path exist for their graph? Explain specifically using the label and degree of each vertex.

Does an Euler circuit exist for their graph? Explain specifically using the label and degree of each vertex.

4) Consider your graph with the perspective of a Hamiltonian path or circuit and explain the following:

In your own words, explain what is required for a path or circuit to be an Euler path or circuit.

Identify one sequence of vertices that makes either a Hamiltonian path or a Hamiltonian circuit.

5) Based on your real-world situation, think about whether it would be most practical to seek an Euler vs. Hamiltonian path or circuit. Which one do you think would be more useful in your situation and why?