Give an example of a connected undirected graph that contains at least twelve vertices that contains at least two circuits. Draw that graph labeling the vertices with letters of the alphabet. Determine one spanning tree of that graph and draw it$.$ Determine whether the graph has an Euler circuit. If so$,$ specify the circuit by enumerating the vertices involved. Determine whether the graph has an Hamiltonian circuit path. If so$,$ specify the circuit by enumerating the vertices involved.