A hierarchical structure of the quad-cube and the associated diameter, domination, and Hamiltonicity

Abstract

The quad-cube is a special case of the metacube that itself is derivable from the hypercube. It is amenable to an application as a network topology, especially when the node size exceeds several million. This paper presents a sequence of graphs, leading up to the quad-cube, where the graphs in the sequence are important in their own right. For example, they exhibit hypercube-like low diameters and efficient domination parameters, and most of them admit a Hamiltonian cycle. The hierarchy is likely to be useful in the future.