Fault-tolerant hamiltonian connectedness of cycle composition networks

It is important for a network to tolerate as many faults as possible. With the graph representation of an interconnection network, a k-regular hamiltonian and hamiltonian connected network is super fault-tolerant hamiltonian if it remains hamiltonian after removing up to k − 2 vertices and/or edges and remains hamiltonian connected after removing up to k − 3 vertices and/or edges. Super fault-tolerant hamiltonian networks have an optimal flavor with regard to the fault-tolerant hamiltonicity and fault-tolerant hamiltonian connectivity. For this reason, a cycle composition framework was proposed to construct a (k + 2)-regular super fault-tolerant hamiltonian network based on a collection of n k-regular super fault-tolerant hamiltonian networks containing the same number of vertices for n ⩾ 3 and k ⩾ 5. This paper is aimed to emphasize that the cycle composition framework can be still applied even when k = 4.