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

This graph does not have Eulerian circuit,but it have Eulerian trail.

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

and ecah vertex doesnot have even degree, so this graph does not have Eulerian circuit.

and there are only two vertices of the graph have odd degree,the G have Eulerian path.

that path is cdefghbagcf.