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Homework Help
Calculus and Beyond Homework Help
Proving the Even Degree Property of Vertices in Closed Trails
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[QUOTE="tarheelborn, post: 4492765, member: 196337"] [h2]Homework Statement [/h2] All vertices in a closed trail have even degree. [h2]Homework Equations[/h2] [h2]The Attempt at a Solution[/h2] Intuitively, I know this statement is true, but I can't seem to see a clear way to show it. I know that a closed trail is a path that connects vertices, so one would follow an edge through a vertex to another edge, thus indicating that, on this particular path, this particular vertex has degree two. Clearly, a non-closed trail has endpoints which must have odd degree because they reach a stopping point on the trail, with a vertex incident to only one edge. Will you please help me put these facts into a coherent proof? Thank you. [/QUOTE]
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Calculus and Beyond Homework Help
Proving the Even Degree Property of Vertices in Closed Trails
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