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.
•Applications of Hamiltonian cycles are given in the introduction.•Rectangular representation is constructed to help finding the solution since it gives a clear visualization of the network.•The first 2 edge disjoint Hamiltonian cycles are constructed based on the rectangular representation.•The third Hamiltonian cycle is first divided into two cases, when norm is odd or even, and then it is constructed.