? into a graph with an Euler circuit by adding a single edge. 1. Any graph with an Euler trail that is not an Euler circuit can be made ? ✓2. If a graph has an Euler trail but not an Euler circuit, then every Euler trail must start at a vertex of odd degree. ? number of vertices. ? ? 3. If a complte graph has an Euler circuit, then the graph has an odd 4. Every graph in which every vertex has even degree has an Euler circuit. ✓ 5. Every graph with an Euler trail is connected.

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