Let Δ be a one-dimensional simplicial complex on { 1 , 2 , ... , s } and S the polynomial ring K [ x 1 , ... , x s ] over a field K. The explicit formula for a 0 (S / I Δ n) is presented when girth (Δ) ≥ 4. If girth (Δ) = 3 we characterize the simplicial complexes Δ for which a 0 (S / I Δ n) = 3 n − 1 or 3 n − 2.