graphs and trees conceptual

Question

Answer 1

There are k Components comprising a total of n vertices. To form each of the component, you need to add vertices to it. 

Only after adding the first vertex in each of the k components, none of the edge is introduced. For the rest of the vertices, an edge is introduced.

So, total number of edges will be n-k i.e.option (B)

Comments

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Why do we need to add edges ? 

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Consider you are constructing that component from the scratch. First, you will add a vertex that will not involve any edge but as soon as you add a new vertex to it a new edge will be added.