Explain why the graph shown in Fig. 31 has neither Hamilton circuits nor Hamilton paths

Step 1 of 2

To show that the graph shown in Fig. 31 has neither Hamilton circuits nor Hamilton paths.

It is known that Hamilton path in a connected graph is a path that visits all the vertices of the graph once and only once.

The graph has no Hamilton paths since the path has to start at either  or  and end at the other one, (no way to start and end) and there is no way to visit the other five vertices without going through some vertices more than once. Note that this graph has two odd vertices, so we know that it has an Euler path.