All double generalized Petersen graphs are Hamiltonian

Abstract

The double generalized Petersen graph DP(n,t), n≥3 and t∈Zn∖{0}, 2≤2t<n, has vertex-set {xi,yi,ui,vi∣i∈Zn}, edge-set {{xi,xi+1},{yi,yi+1},{ui,vi+t},{vi,ui+t},{xi,ui},{yi,vi}∣i∈Zn}. These graphs were first defined by Zhou and Feng as examples of vertex-transitive non-Cayley graphs. Then, Kutnar and Petecki considered the structural properties, Hamiltonicity properties, vertex-coloring and edge-coloring of DP(n,t), and conjectured that all DP(n,t) are Hamiltonian. In this paper, we prove this conjecture.