Recall Joe from who runs a gym-cleaning service. Joe is also responsible for locking the doors of four other gyms. 

(a) Represent each floor plan as a graph. Use the letters shown to label the vertices of the graph and use the letter O to label the vertex that represents the outside of the gym. Place vertex O near where the word Outside is placed in the diagram.

(b) Determine (state yes or no) whether it is possible for Joe to move through the gym using each doorway of the gym exactly one time. In other words, does an Euler path exist in the graph?

(c) If your answer to part (b) is yes, determine one such Euler path.

NY Fitness

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B Outside D E