For a graph to have an Eulerian circuit

$($

a circuit that traverses every edge exactly once and ends at the starting vertex

$)$

$,$

$$every vertex must have an even degree.

In your description, you provided the degrees of each vertex:

A:

$4$

$$degrees

B:

$2$

$$degrees

C:

$4$

$$degrees

D:

$3$

$$degrees

E:

$2$

$$degrees

F:

$1$

$$degree

add least number of edges to make it a euler circuit