Euler and Hamiltonian paths and circuits $(20$ points$)$

a$)$ Does the following graph contain an Euler circuit? If it does, write down the Euler circuit by listing the vertices in the order that they are visited, starting and ending at vertex $D.$ If it does not, explain why.

b$)$ does the graph above in part a$)$ have a Hamiltonian circuit? If it does, write down the Hamiltonian circuit by listing the vertices in the order that they are visited, starting and ending at vertex $B.$ If it does not, explain why.

c$)$ The graph below has an Euler path, but not an Euler circuit. Write down the Euler path, starting at a correct vertex and by listing the vertices in the order that they are visited. Also explain why it doesn't have an Euler circuit.

d$)$ Does the graph below have a Hamiltonian circuit? If it does, write down the Hamiltonian circuit by listing the vertices in the order that they are visited, starting and ending at a vertex of your choosing. If it does not, explain why.