Maths Olympiad Prep

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Combinatorics Difficulty 4.9 AIME Find the answer

How many different graphs with 9 vertices exist where each vertex is connected to 2 others?

A number or a short expression. Spacing and $ signs are ignored.

Solution

It suffices to consider the complements of the graphs, so we are looking for graphs with 9 vertices, where each vertex is connected to 2 others. There are 4\mathbf{4} different graphs.

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