I was going through graph theory and came across the term Euler path or some people prefer Euler trail as vertices can repeat.
According to the definition from wiki (https://en.wikipedia.org/wiki/Eulerian_path), Euler path is defined as under
In graph theory, a Eulerian trail (or Eulerian path) is a trail in a graph which visits every edge exactly once.
Following are the conditions for Euler path,
An undirected graph (G) has a Eulerian path if and only if every vertex has even degree except 2 vertices which will have odd degree, and all of its vertices with nonzero degree belong to a single connected component.
So as per the definition, I need to cover all edges in a connected graph with non zero degrees.
The same information is stated here at geeks for geeks(https://www.geeksforgeeks.org/eulerian-path-and-circuit/).
so if I need to only consider vertices with non zero degrees then graph (G)can be disconnected?
Note: These are the other information I collected from the wiki page
1)Finite connected graph (with vertices of even degree except 2 or 0 with the odd degree) will have a Euler path. 2)But Euler path can also be present in the disconnected graph as shown in the following picture
3) Doubt does following graph have Euler path,
My answer ,No as all vertices are not in same connected component.