Edge disjoint Hamiltonian cycles in Eisenstein-Jacobi networks

Many communication algorithms in parallel systems can be efficiently solved by obtaining edge disjoint Hamiltonian cycles in the interconnection topology of the network. The Eisenstein-Jacobi (EJ) network generated by α=a+bρ, where ρ=(1+i3)/2, is a degree six symmetric interconnection network. The hexagonal network is a special case of the EJ network that can be obtained by α=a+(a+1)ρ. Generating three edge disjoint Hamiltonian cycles in the EJ network with generator α=a+bρ for gcd(a,b)=1 has been shown before. However, this problem has not been solved when gcd(a,b)=d>1. In this paper, some results to this problem are given.