Edge disjoint Hamiltonian cycles in Eisenstein–Jacobi networks

Abstract

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.