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Asked: 2026-06-18T04:52:52+00:00

Basically, you require n-1 edges, to make a connected graph with n nodes. I

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Basically, you require n-1 edges, to make a connected graph with n nodes. I would like to know if there is any theory behind finding the number of distinct ways you can select the n-1 edges, from the total n(n-1)/2 edges that are possible, such that the graph remains connected.

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  1. Editorial Team

    There are exactly nn-2 connected graphs with vertex set {1,...n} for n > 0. This result is known as Cayley’s Formula.

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