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trees have no cycles, by definition, a tree has no interior faces, and there only exist an exterior face. This gives |F| = 1. Plugging in these values into the equation, we have |V|- |E| + |F| = |E| + 1-|E| + 1 = 2, so Euler’s Theorem holds when G is a tree. Case 2: G(V, E) contains cycles. In this