Aspire Faculty ID #18574 · Topic: UGC NET Computer Science Dec 2022 Shift I (Paper II) · Just now
UGC NET Computer Science Dec 2022 Shift I (Paper II)

Let $G$ be a simple, undirected graph with $n$ vertices and $k$ connected components. What is the minimum possible number of edges of $G$?

Solution

For a connected component with $m$ vertices, minimum edges required:

$m-1$

If graph has $k$ connected components, then minimum total edges:

$=(n_1-1)+(n_2-1)+...+(n_k-1)$

$=(n_1+n_2+...+n_k)-k$

$=n-k$

Correct option is:

$\boxed{(d)\ n-k}$

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