is it necessary to cover all the verticies in eular path?
It really comes down to your definition of an Euler trail. The one I'm familiar with is similar to the one on Wikipedia:


  An Euler trail is a trail (path that allows repeats) that uses every edge exactly once.


With this definition, an Euler trail doesn't have to touch every vertex: if there's a vertex with no edges, the Euler trail doesn't have to go anywhere near it.

However, if there's a vertex with positive degree, and another vertex with positive degree, and they're not (weakly) connected, then there can be no Euler trail. Because if you use the edges on one, there's no way to reach the edges on the other.