Definition: A graph having Euler Path is called as Euler edge.
Sometimes Euler path is also called as Euler Circuit.
So, what is Euler path or Euler Circuit?
A path which starts and ends at same vertex is called as Euler Path. It means, you need to visit all the edges only one.
Note: A vertex can be repeated but edge cannot be repeated.
Let us understand Euler Graph with help of an example:
Here we can traverse
1 -> 2 -> 3 -> 4 -> 2 -> 5 -> 1
Here we started at vertex 1 and traversed all the edges only once and ended at vertex 1 again.
Hence this graph has Euler circuit. Hence it is a Euler graph.
Below are the conditions for a graph to be a Euler Graph:
- All the vertices in the graph should have even degree.
- A graph has a with vertex with 0 degree, then also it is considered as Euler Graph.
Semi Euler Graph:
In a graph, if we are able to visit all the edges, but cannot return to the starting vertex is called as semi Euler graph.
Here we can go from
1 -> 2 -> 3 -> 4 -> 5 -> 6.
Here we have visited all the edges, but did not return at the starting edge. Hence it is a semi Euler graph.
Properties of Semi Euler Graph:
All the vertices have even degree, except for 2 vertices, it will have odd degree.