Abstract
The n-dimensional Manhattan network Mn—a special case of n-regular digraph—is formally defined and some of its structural properties are studied. In particular, it is shown that Mn is a Cayley digraph, which can be seen as a subgroup of the n-dim version of the wallpaper group pgg. These results induce a useful new presentation of Mn, which can be applied to design a (shortest-path) local routing algorithm and to study some other metric properties. Also it is shown that the n-dim Manhattan networks are Hamiltonian and, in the standard case (that is, dimension two), they can be decomposed in two arc-disjoint Hamiltonian cycles. Finally, some results on the connectivity and distance-related parameters of Mn, such as the distribution of the node distances and the diameter are presented.
Published Version
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