English

Distance Regular Colorings of $n$-Dimensional Rectangular Grid

Combinatorics 2014-12-25 v1

Abstract

We study the infinite graph of nn-dimensional rectangular grid that doesn't appear distance regular and the distance regular colorings of this graph, which are defined as the distance colorings with respect to completely regular codes. It is proved that the elements of the parameter matrix of an arbitrary distance regular coloring form two monotonic sequences. It is shown that every irreducible distance regular coloring of the nn-dimensional rectangular grid has at most 2n+12n+1 colors.

Keywords

Cite

@article{arxiv.1412.7665,
  title  = {Distance Regular Colorings of $n$-Dimensional Rectangular Grid},
  author = {Sergey Avgustinovich and Anastasia Vasil'eva},
  journal= {arXiv preprint arXiv:1412.7665},
  year   = {2014}
}

Comments

7 pages. The results were presented in part at the 13th International Workshop on Algebraic and Combinatorial Coding Theory

R2 v1 2026-06-22T07:43:18.641Z