QUESTION 1 Let G be a directed multigraph. (a) A directed circuit of G is a circuit on G which traverses every edge in the given direction. A directed Euler circuit is a directed circuit which traverses every edge exactly once. Show that G has a directed Euler circuit if and only if G is connected and id(V)-od(v) for every vertex v of G. (b) Define the notions of a directed trail and a directed Euler trail similarly and give a necessary and sufficient condition for G to have a directed Euler trail but no directed Euler circuit