(a) Let G = (V, E) be a directed graph or multigraph with no isolated vertices. Prove that G has a directed Euler circuit if and only if G is connected and od(v) = id(v) for all v ∈ V.
(b) A directed graph is called strongly connected if there is a directed path from a to b for all vertices a, b, where a ≠ b. Prove that if a directed graph has a directed Euler circuit, then it is strongly connected. Is the converse true?