The classification of hamiltonian generalized Petersen graphs

Abstract The generalized Petersen graph GP( n , k ), n ≥ 2 and 1 ≤ k ≤ n − 1, has vertex-set { u 0 , u 1 ,…, u n − 1 , v 0 , v 1 ,…, v n − 1 } and edge-set { u i u i + 1 , u i v i , v i v i + k : 0 ≤ i ≤ n − 1 with subscripts reduced modulo n }. In this paper it is proved that GP( n , k ) is hamiltonian if and only if it is neither GP (n, 2) ≅ GP (n, n − 2) ≅ GP (n, (n − 1) 2 ≅ GP (n, (n + 1) 2 ) when n ≡ 5 (mod 6) nor GP (n, n 2 ) when n ≡ 0 (mod 4) and n ≥ 8.