Will a complete graph with 2 vertices have an Euler circuit? With 3 vertices? With 4 vertices? With 5 vertices? With n vertices?
Investigate and summarize your findings. Explain your process and your reasoning.

You have been hired by the city as a deputy street supervisor. Part of your job is to inspect city streets for potholes. Your area of inspection is shown on the given street map. Devise a plan for street inspection that starts at your office, inspects each block at least once, ends at your office, and takes the least amount of time (time is money). Assume it takes five minutes to walk a block for inspections including corners and one minute to just walk a block without inspecting (called deadheading). (See attached task.)

Example Documents:

• Problem-Based Instructional Task [ .doc ]

Determine if the following vertex-edge graph has an Euler circuit or path. If there is an Euler circuit or path, find it. If there is not an Euler circuit or path, explain why not.

The street network of a city can be modeled with a graph in which the vertices represent the street corners, and the edges represent the streets. Suppose you are the city street inspector and it is desirable to minimize time and cost by not inspecting the same street more than once.