What is the Eulerian trail in math?

What is the Eulerian trail in math?

A Eulerian Trail is a trail that uses every edge of a graph exactly once and starts and ends at different vertices. A Eulerian Circuit is a circuit that uses every edge of a network exactly one and starts and ends at the same vertex.

Is there a Euler trail?

An open walk which visits each edge of the graph exactly once is called an Eulerian Walk. Since it is open and there is no repetition of edges, it is also called Eulerian Trail.

Where is the Eulerian trail?

Fleury’s Algorithm for printing Eulerian Path or Circuit

1. Make sure the graph has either 0 or 2 odd vertices.
2. If there are 0 odd vertices, start anywhere. If there are 2 odd vertices, start at one of them.
3. Follow edges one at a time.
4. Stop when you run out of edges.

What is the difference between a Euler trail and a Euler circuit?

A trail in a graph G is said to be an Euler trail when every edge of G appears as an edge in the trail exactly once. An Euler circuit is a closed Euler trail. A graph is said to be Eulerian if it has an Euler circuit.

How do you know if you have a Eulerian trail?

If there are no vertices of odd degree, all Eulerian trails are circuits. If there are exactly two vertices of odd degree, all Eulerian trails start at one of them and end at the other.

How do you determine Euler path or circuit?

Euler’s Theorem: If a graph has more than 2 vertices of odd degree then it has no Euler paths. 2. If a graph is connected and has 0 or exactly 2 vertices of odd degree, then it has at least one Euler path 3. If a graph is connected and has 0 vertices of odd degree, then it has at least one Euler circuit.

What is an open Euler trail?

A trail in a connected graph G which originates in one stops in another vertex and contains all edges of G is called an open eulerian trail. We say that each such graph can be drawn in a single stroke.

What makes a Euler path?

An Euler path is a path that uses every edge of a graph exactly once. An Euler circuit is a circuit that uses every edge of a graph exactly once. ▶ An Euler path starts and ends at different vertices. ▶ An Euler circuit starts and ends at the same vertex.