Distance Regular Colorings of $n$-Dimensional Rectangular Grid
Combinatorics
2014-12-25 v1
Abstract
We study the infinite graph of -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 -dimensional rectangular grid has at most colors.
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