In this note, we obtain a new method of proving a Cayley graph can whether or not be decomposed into Hamiltonian circuits and use this method, we prove that if a group G has some special properties, then Cayley graph (G,M) can be decomposed into two Hamiltonian circuits. This result answers a partial case of Alspach's conjecture concerning Hamiltonian decomposition of 2k-regular connected Cayley graphs.
This paper discusses a class of vertex-transitive digraphs.It is shown that these digraphs are rational and can be decomposed into Hamiltonian dicycles.
