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2022 SSMO Accuracy Round Problems/Problem 9

Revision as of 13:04, 14 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== The graph <math>\Gamma</math> has <math>52</math> vertices labeled <math>A, A', B, B', \dots, Z, Z'</math>, such that <math>A</math> is not connected to <math>A'</...")
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Problem

The graph $\Gamma$ has $52$ vertices labeled $A, A', B, B', \dots, Z, Z'$, such that $A$ is not connected to $A'$, $B$ is not connected to $B'$, and so on. Suppose that all the vertices other than $A'$ have different degrees (number of connections to the vertex). Find the sum of all possible values for the number of edges (connections) in $\Gamma$.

Solution

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