Fault-tolerant cycle embedding in dual-cube with node faults

A low-degree dual-cube was proposed as an alternative to the hypercubes. A dual-cube DC(m) has m + 1 links per node, where m is the degree of a cluster (m-cube) and one more link is used for connecting to a node in another cluster. There are 2 clusters and hence the total number of nodes in a DC(m) is 2 + . In this paper, by using Gray code, we show that there exists a fault-free cycle containing at least 2 + 1 – 2f nodes in DC(m), m ≥ 3, with f ≤ m faulty nodes.