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# D1 Edexcel

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1. Can someone please explain this question a bit further and show me how they worked it out without using the same thing they did in the book Thank you.

" Prove that there must always be an even (or zero) number of vertices with odd valency in every graph"

Thank you ~ Noah.
2. It's the handshaking lemma. Each arc contributes 2 to the valency, so the sum of the valencies must be even. So you can't have an odd number of nodes with odd valency; in that case the sum of the valencies would be odd.
3. (Original post by NotNotBatman)
It's the handshaking lemma. Each arc contributes 2 to the valency, so the sum of the valencies must be even. So you can't have an odd number of nodes with odd valency; in that case the sum of the valencies would be odd.
So for the exam do I only really need to understand for hand shaking lemma that The total valency/degree is double the total arcs/edges ?
4. (Original post by NoahMal)
So for the exam do I only really need to understand for hand shaking lemma that The total valency/degree is double the total arcs/edges ?
Yes.

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