#### Answer

The graph has an Euler path but not an Euler circuit.

#### Work Step by Step

According to Euler's theorem, for a connected graph to have at least one Euler path, the number of odd vertices must be either 0 or 2. For a connected graph to have at least one Euler circuit, the number of odd vertices must be 0.
The connected graph has exactly two odd vertices. Therefore, by Euler's theorem, the graph has at least one Euler path but no Euler circuits.