Question 1.102

72. Answer the following questions for accompanying graph G, which is used to model roads that must be inspected for potholes.

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  1. How many odd-valent vertices does G have?
  2. If G has an Euler circuit, write it down.
  3. If G does not have an Euler circuit, what is the minimum number of edges that must be repeated to find a tour of G that starts and ends at C and traverses each edge of G at least once?
  4. How does your answer to part (c) relate to the answer to part (a)?