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? 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.

? 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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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? 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.
Transcribed Image Text:? 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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