Proof
(related to Lemma: Handshaking Lemma for Finite Graphs)
- In any graph \(G(V,E,\gamma)\), each edge has two ends.
- Thus, it contributes exactly \(2\) to the sum of the vertex degrees, which is well-defined, if the graph is finite.
- It follows $$\sum_{v\in V}\deg_G(v)=2|E|.$$
∎
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References
Bibliography
- Aldous Joan M., Wilson Robin J.: "Graphs and Applications - An Introductory Approach", Springer, 2000
