KöMaL problem A, 2022

Combinatorics Difficulty 7.0 National Olympiad, round 2 Prove it Hungary

Let $G$ be an arbitrarily chosen finite simple graph. We write non-negative integers on the vertices of the graph such that for each vertex $v$ in $G$ the number written on $v$ is equal to the number of vertices adjacent to $v$ where an even number is written. Prove that the number of ways to achieve this is a power of 2.

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