Some Properties in Multidimensional Multivalued Discrete Torus

摘要

Current research concerns the following issues: n-dimensional discrete torus generated by cycles of even length is considered; the concept of standard arrangement in the torus is defined and some basic properties of this arrangement are investigated. The issues considered are similar to discrete isoperimetry constructions, being related to concept of neighbourhood in terms of linear arrangements of vertices. Considered are the basic properties of solving the discrete isoperimetry problem on torus.