= {V1, V2, V3,, Un}, 10. Let G = (V,E) be a loop-free connected undirected graph where V n ≥ 2, deg(v1) = 1, and deg(vi) ≥ 2 for 2≤ i ≤n. Prove that G must have a cycle.

10. Type the answer perfectly and don't use ChatGPT.

Let G = (V, E) be a loop-free connected undirected graph where V = {v₁, v₂, v₃, . . . , v_n},
n ≥ 2, deg(v₁) = 1, and deg(vi) ≥ 2 for 2 ≤ i ≤ n. Prove that G must have a cycle.