HAMILTONIAN DECOMPOSITION OF CAYLEY GRAPHS OF ORDERS p~2 AND pq

In this paper, it is proved that any connected Cayley graph on an abelian group of order pq or p~2 has a hamiltonian decomposition, where p and q are odd primes. This result answers partially a conjecture of Alspach concerning hamiltonian decomposition of 2k-regular connected Cayley graphs on abelian groups.