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Unit 1 · Discrete Structures and Optimization Paper 2 CS · December 2022 Shift 1

Let G be a simple undirected graph with n (n > 10) vertices and k connected components. What is the minimum possible number of edges of G?

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Correct answer: D. n − k

Explanation

Each component with nᵢ vertices needs at least nᵢ − 1 edges (a tree). Σ(nᵢ − 1) = n − k.

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