Two-node-Hamiltonicity of enhanced pyramid networks

An enhanced pyramid network is an alternate hierarchical structure for a pyramid network. This structure is created in a pyramid network by replacing each mesh with a torus at layers greater than one. This work studies the fault-tolerant Hamiltonian problem on the enhanced pyramid network and demonstrates that an enhanced pyramid network with two faulty nodes is Hamiltonian. The result is optimal, because edge connectivity and node connectivity of the enhanced pyramid network are both 4.