**Euler Trail but not Euler Tour**

Conditions:

- At most 2 odd degree (number of odd degree <=2) of vertices.
- Start and end nodes are different.

**Euler Tour but not Euler Trail**

Conditions:

- All vertices have even degree.
- Start and end node are same.

**Euler Tour but not Hamiltonian cycle**

Conditions:

- All edges are traversed exactly once.
- Some nodes (vertices) are traversed more than once.

**Hamiltonian cycle but not Euler Tour**

Conditions:

- All nodes are traversed exactly once.
- Some edges are traversed more than once.

**Euler Trail but not Hamiltonian cycle**

Conditions:

- Vertices have at most two odd degree.
- Some nodes are traversed more than once.
- Start and end node is not same.

**Hamiltonian cycle but not Euler Trail**

Conditions:

- Start and end node is same.
- Some edges is not traversed or no vertex has odd degree.

**This graphs are very very important for any examinations.**