A unique arithmetic labeling of hexagonal lattices | Zendy

Chang Gerard J. | Zendy; Hwang F. K. | Zendy; Wright P. E. | Zendy; Griggs J. R. | Zendy

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A unique arithmetic labeling of hexagonal lattices

Author(s) -

Chang Gerard J.,

Hwang F. K.,

Wright P. E.,

Griggs J. R.

Publication year - 1995

Publication title -

journal of combinatorial designs

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.618

H-Index - 34

eISSN - 1520-6610

pISSN - 1063-8539

DOI - 10.1002/jcd.3180030303

Subject(s) - modulo , combinatorics , hexagonal crystal system , mathematics , equivalence (formal languages) , set (abstract data type) , arithmetic , discrete mathematics , computer science , chemistry , crystallography , programming language

Consider an r ‐layer hexagon consisting of 3 r 2 + 3 r + 1 hexagonal cells. Can one label the cells by the set N r = {0,1,…, 3 r 2 + 3 r } such that each line of adjacent cells are labeled by numbers forming an arithmetic progression modulo (3 r 2 + 3 r + 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. © 1995 John Wiley & Sons, Inc.

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