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Show that the number of labelled simple graphs with n vertices is 2n(n-1)/2. (By Induction)

Show that the number of labelled simple graphs with n vertices is 2n(n-1)/2. (By Induction)

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Suppose we want to join a vertex with no vertex of a graph having n-1 vertices, the number of ways of doing this is only 1.suppose we want to join this vertex to exactly one vertex of graph having n-1 vertices, the number of ways in which this can be done is exactly n-1 and so on.

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