Hello people, I need your help as soon as possible. I will be very thankful to everyone engaged in my math problem:

We have an end undirected graph (not infinite) and every vertex in that graph has odd degree. Prove that every edge is in even number Hamiltonian cycles (including 0).

We have an end undirected graph (not infinite) and every vertex in that graph has odd degree. Prove that every edge is in even number Hamiltonian cycles (including 0).

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