1.If the graph is connected and has exactly 2 odd degree vertices then there exists at least one Euler Path.Mainly it starts with one end and ends on the other End.
1.If the graph is connected and every vertex has even degree then the Graph has atleast one Euler Circuit.
Euler Circuit is a part of Euler Path but Converse is nt True.
# of ODD Vertices
Implication (for a connected graph)
There is at least
one Euler Circuit.
THIS IS IMPOSSIBLE!
There is no Euler Circuit but at least 1 Euler Path.
more than 2
There are no Euler Circuits
or Euler Paths.
Eulerian Path is a path in graph that visits every edge exactly once. Eulerian Circuit is an Eulerian Path which starts and ends on the same vertex.
A directed graph has an eulerian cycle if following conditions are true.
1) All vertices with nonzero degree belong to a single strongly connected component.
2) In degree and out degree of every vertex is same.