You have six errands to run around​ town, in no particular o…

You have six errands to run around​ town, in no particular order. You plan to start and end at home. You must go to the post office​ (P), deposit a check at the bank​ (B), drop off dry cleaning​ (D), visit a friend at the hospital (H), get a flu shot at the medical clinical (M), and pick up a groceries at the store (G). A weighted graph is shown with the distances​ (in miles) to the locations shown on the edges. If each Hamilton circuit represents a route to run your​ errands, how many different routes are​ possible? Enter a numerical answer.   

A connected graph has 94 even vertices and no odd vertices. …

A connected graph has 94 even vertices and no odd vertices.   Determine whether the graph has an Euler path​ (but not an Euler​ circuit), an Euler​ circuit, or neither an Euler path nor an Euler​ circuit, and explain why. By​ Euler’s theorem, this is because the graph has