  The Hamiltonian cycle problem (HCP) in digraphs D with degree bound two is
solved by two mappings in this paper. The first bijection is between an
incidence matrix C_{nm} of simple digraph and an incidence matrix F of balanced
bipartite undirected graph G; The second mapping is from a perfect matching of
G to a cycle of D. It proves that the complexity of HCP in D is polynomial, and
finding a second non-isomorphism Hamiltonian cycle from a given Hamiltonian
digraph with degree bound two is also polynomial. Lastly it deduces P=NP base
on the results.
