Weighted distance on the m-dimensional extensions of the face-centered cubic lattice

Abstract

The face-centered cubic lattice is one of the most common and most known three-dimensional structure appearing in the nature. Its higher dimensional extensions are interesting not only from algebraic and combinatorial points of view, but also in geometry, in physics and in material science. In this paper, digital, i.e., path-based, distances are computed in the m-dimensional generalizations of this face-centered cubic lattice. In the graphs of these m-dimensional lattices, the two usual types of neighborhood relations of the face-centered lattice are also used implying the use of two different weights. A method based on operational research is used to identify some shortest weighted paths and thus, to derive formula for the weighted distance depending on the weights.