Maths Olympiad Prep

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Problem 984

AMC 12 late, AIME early
Combinatorics Difficulty 4.9 Find the answer HMMT February

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

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official 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.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.