Interactive practice questions
The following questions relate to Eulerian trails and semi-Eulerian trails.
Which of the following is a correct description of an Eulerian trail?
A trail that passes through each edge of a graph at least once.
A trail that passes through each edge of a graph exactly once and starts and finishes at the same vertex.
A trail that visits each edge and each vertex once only.
A closed trail that visits each vertex exactly once.
Which of the following is a correct description of a semi-Eulerian trail?
An Eulerian trail that starts and finishes at the same vertex.
An Eulerian trail that visits each vertex exactly once.
A trail that passes through each vertex of the graph and starts and finishes at a different vertex.
A trail that passes through each edge of the graph and starts and finishes at a different vertex.
Which condition is required for an Eulerian trail to exist?
Which condition is required for a semi-Eulerian trail to exist?
In order to traverse a graph which has an Eulerian trail, which vertex should one start at?