A unique arithmetic labeling of hexagonal lattices

摘要

AbstractConsider anr‐layer hexagon consisting of 3r2+ 3r+ 1 hexagonal cells. Can one label the cells by the setNr= {0,1,…, 3r2+ 3r} such that each line of adjacent cells are labeled by numbers forming an arithmetic progression modulo (3r2+ 3r+ 1) (in proper ordering)? We show that for eachrthere exists such a labeling unique up to equivalence. We also study some other related issues. © 1995 John WileySons,