Vertex transitivity, distance metric, and hierarchical structure of the dual-cube
Pranava K. Jha · The Journal of Supercomputing · 2022
Abstract The dual-cube, derivable from the hypercube, admits a number of good properties that render it as a good network topology, especially when the node size exceeds several million. This paper presents several other welcome characteristics of the graph. Prominent among them are: (1) vertex transitivity that facilitates the working of an algorithm meant for a “local” context in the global context as well, (2) an exact formula for the distance between two nodes, which leads to a precise result on the distance-wise node distribution of the graph and an exact formula for the average node distance, and (3) a hypercube-like hierarchical structure of the graph that is amenable to an inductive treatment.