A Unified Constant-Time Switch Rule for Constructing Edge-Disjoint Hamiltonian Cycles in Gaussian Networks (opens in new tab)

Gaussian networks are degree-four symmetric interconnection networks defined over residue classes of Gaussian integers. Earlier work showed that when the generator $\alpha=a+bi$ satisfies $\gcd(a,b)=1$, the real and imaginary dimensions directly form two edge-disjoint Hamiltonian cycles. A later construction extended the result to the non-coprime case $\gcd(a,b)=d>1$, but its proof used long node-sequence tables and separate odd/even cases for $...