A note on Generalized Petersen Graphs

We give an alternative constructive proof of a theorem of M. Watkins, F. Castagna and G. Prins, i.e., the generalized Petersen graphs are of class one, except the Petersen graph. As a consequence, we obtain some bounds for the regular genus of these graphs and give a partial solution to a conjecture stated in [F. Castagna, G.Prins, Pacific J. Math. 40, 1972]