a forest, its subgraphs, components, number of edges

On our practice exam, our teacher gave us this problem and this solution:

Let $G$ be a forest with $k \geq 1$ components. What type of (sub)graph is each component? Suppose each component has $n_i$ vertices with $n_i \geq 1$. How many edges does $G$ have? (Show your work!)

ANSWER: Each component is a tree. Suppose there are $c$ components. Then $|E(G)| =\sum_{i=1}^c n_i − 1 = |V(G)| − c$.

I am confused as to how she got that answer. I do not understand how she knows to use that summation for the number of edges.

2022-07-25 20:43:33
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