Prove that: for a graph, G = (V, E) that I ⊆ V is the largest independent set if and only if V − I isthe smallest edge cover.

Question

Prove that: for a graph, G = (V, E) that I ⊆ V is the largest independent set if and only if V − I isthe smallest edge cover.
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Solution 1

To prove this statement, we need to understand the definitions of independent set and edge cover in a graph.

  1. Independent Set: An independent set in a graph is a set of vertices where no two vertices are adjacent. In other words, there is no edge between any two vertices in the set.

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