How can I calculate the number of vertices of a tree knowing he has 33 vertices of degree 1, 25 vertices of degree 2, 15 vertices of degree 3 and all other vertices of grade 4?
2026-03-27 13:38:17.1774618697
Graph theory: tree vertices
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You know that for a tree it holds $$\sum_{v\in V} d(v) = 2|E| = 2(|V|-1) $$
Now you know that there are $|V|-(33+25+15)$ vertices of degree $4$ and therefore:
$$ 33\cdot 1 + 25 \cdot 2 + 15\cdot 3 + [|V|-73]\cdot 4 = 2|V| - 2$$ Now just find the value of $|V|$.