Which of the following graphs have Euler circuits, Euler trails, or neither?

Question

Which of the following graphs have Euler circuits, Euler trails, or neither?

I tried :Euler Trails [A,B,C,A,D,B,C]

I tried :Euler Trails [A,B,D,E,G,F,D,C,A,D,G]

but I am confused about Euler circuits.

Answer 1

Your answer for (a) is wrong. An Euler Circuit occurs when there are no vertices of odd degree. An Euler trail can occur when there are exactly two vertices of odd degree. Graph (a) is $K_{4}$, which is $3$-regular. So there is no Eulerian trail or circuit.

For (b), there are exactly two vertices of odd degree. Vertices (a) and (g) both have degree $3$.