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Please see attached image for the graph.
a. Yes, it is mathematically possible because the degree of vertices for P=3, T=3, M=2, C=4, and R=2 and in Euler’s theorem, the graph has to be connected, which in this case it is and the number of vertices in the graph whose vertices is odd, is 0 or 2. And in this case, we have 2 that have a degree of vertices that are odd, therefore mathematically this is possible for the driver. The route would be P > R > C > M > T > C > P > T.
b.
<span>It is mathematically possible. The router would be P
> C > R > T > M > C > T. Essentially, you travel each road
once.
</span>
c. The driver would use a Hamiltonian circuit. The route would be J > R > A > C > V > M > T > P > J.
Therefore, if
Therefore, the dimensions of this rectangle are 15 and 2.