In an Euler graph, a trail that visits every edge exactly once is called:a.Hamiltonian cycleb.Eulerian cyclec.Eulerian pathd.Hamiltonian path

To answer the question regarding Euler graphs, let's clarify the definitions:

1. Eulerian Cycle: A closed trail in a graph that visits every edge exactly once and returns to the starting vertex.
2. Eulerian Path: A trail in a graph that visits every edge exactly once but does not necessarily return to the starting vertex.
3. Hamiltonian Cycle: A cycle that visits every vertex exactly once and returns to the starting vertex.
4. Hamiltonian Path: A path that visits every vertex exactly once but does not necessarily return to the starting vertex.

Final Answer

The correct answer to the question is b. Eulerian cycle. An Eulerian cycle is specifically a trail that visits every edge of the graph exactly once and returns to its starting point, while an Eulerian path is a more general concept where the path may not return to the starting vertex. Therefore, the best term for a trail that visits every edge exactly once, as described in the question, would specifically be an Eulerian cycle.