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Number of graphs with vertex set {1, 2, 3, ..., n}

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The problem is to let V = {1, 2, 3, ..., n}, and to determine the number of different graphs that can be formed with V as vertex set.

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The solution is a step-by-step derivation of the number of graphs with vertices 1, 2, 3, ..., n.

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Two graphs G1, G2 with the same vertex set are different if and only if there is at least one edge in G1 that is not in G2, or at least one edge in G2 that is not in G1, or both.

Every edge of a graph is naturally associated with some unordered pair of vertices (the unordered pair of vertices that are connected by that edge), and no two edges are associated with the same unordered pair of vertices, since there can be at most one edge connecting a given ...

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