This is a Discrete Math question. Please solve it in a detailed way.

9. Show that a directed multigraph having no isolated vertices has an Euler path but not an Euler circuit if and only if the graph is weakly connected and the in-degree and out-degree of each vertex are equal for all but two vertices, one that has in-degree one larger than its out- degree and the other that has out-degree one larger than its (30 pts) in-degree