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yoyobarn
 Post subject: Handshake Theorem for Non-simple graphs
PostPosted: Wed, 6 Jul 2011 09:12:35 UTC 
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Does the Handshake Theorem (sum of degree of vertices is twice the number of edges) apply to non-simple graphs (ie. those with loops and parallel edges)?


Thank you very much for answering this basic question!
(I am a beginner in Graph theory).
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outermeasure
 Post subject: Re: Handshake Theorem for Non-simple graphs
PostPosted: Wed, 6 Jul 2011 09:49:03 UTC 
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yoyobarn wrote:
Does the Handshake Theorem (sum of degree of vertices is twice the number of edges) apply to non-simple graphs (ie. those with loops and parallel edges)?


Thank you very much for answering this basic question!
(I am a beginner in Graph theory).


As long as you count appropriately, yes.

_________________
\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
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yoyobarn
 Post subject:
PostPosted: Wed, 6 Jul 2011 10:57:01 UTC 
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ok thanks a lot, I think i get it..

just realised there was a different counting method for loops.
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