Abstract: It is proved that he lower bound on the crossing number of the generalized Petersen graphs G(2m+1,m) is 3 by deleting edges. Then it showes the crossing number of the generalized Petersen graphs G(2m+1,m) is 3 exactly.

Key words: crossing number of a graph, principal cycle, adjoint principal cycle, the generalized Petersen graph, crossing number of a graph, principal cycle, adjoint principal cycle