Consecutive-magic labeling of generalized Petersen graphs

Abstract

The generalized Petersen graph P(n, k) has vertex set V = { u₁ , u₂ , . . . , u_n , v₁ , v₂ , . . . , v_n } and edge set E = { u_i u_{i + 1} , u_i v_i , v_i v_{i + k} \ for 1 ≤ i ≤ n and 1 ≤ k ≤ [n-1/2], with indices taken modulo n}. We deal with the problem of labeling edges of the generalized Petersen graph P(n, k) and we show that P(n, k) is consecutive-magic iff n is even (n ≥ 4) and k ≤ n/2 - 1.