Graph G has 21 edges, 3 vertices which have a degree of 4, other vertices have a degree of 3. How many vertices are there in total?
(Graph) - How to find number of vertices given number of edges and some information on the degrees of vertices?
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discrete-mathematics
graph-theory
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0Do you know about the handshaking lemma? – 2017-01-31
1 Answers
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We know that the sum of degree across all nodes is equal to twice the number of edges (Handshaking Lemma). Let there be $N$ vertices in this graph.
We have $$ \begin{align} 3 \cdot 4 + 3 \cdot (N-3) &= 2 \cdot 21 \\ 12 + 3 \cdot (N-3)&= 42\\ 3 \cdot (N-3)&= 30 \\ (N-3) &= 10\\ N &= 13\\ \end{align} $$
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0Thank you! I wasn't sure if I could do that so I feel stupid for asking this question. Cheers – 2017-01-31