Supereulerian generalized prisms

For a graph G with vertices labeled 1, 2, ⋯, n and a permutation α in S_n, the symmetric group on {1, 2, ⋯, n}, the α-generalized prism over G, α(G), consists of two copies of G, say G_x and G_y, along with the edges (x_i, y_α(i)), for 1 ≤ i ≤ n. In this note, we consider results of the form that if G has property P, then for any α ∈ S_|V(G)|, α(G) is supereulerian. We proved that if a graph G is 2-edge-connected and has at most 5 vertices of degree 2, then for any α ∈ S_|V(G)|, α(G) is supereulerian if and only if it is not the Petersen graph.