Decide if the following graph has a Eulerian circuit Euleria

Decide if the following graph has a Eulerian circuit, Eulerian trail, or neither. If it does have a Eulerian circuit or trail, give an example. If it has neither, state why this is the case.

Solution

The following graph doesnot have Eulerian circuite and Eulerian trail.

The degrees of each vertex are Deg(a)=3; deg(b)= 2;deg(c)= 3;deg(d)= 2;deg(e)= 2; deg(f)=3; deg(g)=4 ;deg(h)=3.

since the degrees of each vertex is not even,so the graph does not have Eulerian circuite.

and, there are 4 vertex of odd degree, hence it is does not have Eulerian trail.