Solution to Problem 1
We see that the sequence a, b, c, d, e, f, a provides a path from every vertex to every other vertex, so this graph is strongly connected.
Solution to Problem 2
The cycle c, d, e, c guarantees that these three vertices are in one strongly connected component. The vertices a,b, and f are in strong components by themselves, since there are no paths both to and from each of these to every other vertex. Therefore the strongly connected components are {a}, {b}, {c,d,e}, and {f}.
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Solution to Problem 3
We see that each vertex has even degree. Its vertices are strongly connected. This is a directed graph with each vertex has equal in-degree and out-degree. Thus, this graph is with an Euler circuit. This also proves that there exists an Euler path. The sequence a, d, b, d, e, b, e, c, b, a is an example of such an Euler path.
Solution to Problem 4
This graph has no Hamilton circuit. The cut edge {e,f} prevents a Hamilton cir- cuit.
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