A unique arithmetic labeling of hexagonal lattices

✍ Scribed by Gerard J. Chang; F. K. Hwang; P. E. Wright; J. R. Griggs

• Publisher: John Wiley and Sons
• Year: 1995
• Tongue: English
• Weight: 391 KB
• Volume: 3
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.3180030303

✦ Synopsis

Consider an r-layer hexagon consisting of 3r2 + 3r + 1 hexagonal cells. Can one label the cells by the set N, = {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 each r there exists such a labeling unique up to equivalence. We also study some other related issues.