Question: Show that a directed multi graph having no isolated vertices has an Euler path but not an Euler circuit if and only if the graph

Show that a directed multi graph 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 in-degree.

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