On identifying codes in the hexagonal mesh

: Honkala I, Laihonen T

Publisher: ELSEVIER SCIENCE BV

: 2004

: Information Processing Letters

: INFORMATION PROCESSING LETTERS

: INFORM PROCESS LETT

: 89

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: 14

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: 0020-0190

DOI: https://doi.org/10.1016/j.ipl.2003.09.009

It is shown that, if r greater than or equal to 2, there exists an (r, less than or equal to 2)-identifying code in the infinite hexagonal mesh with density (5r + 2)/((r + 2)(2r + 1)) for even r and (5r + 1)/((dr + 1)(2r + 1)) for odd r. The optimal density of a (1, less than or equal to 2)-identifying code in the infinite hexagonal mesh is shown to be 2/3 and the optimal densities of (1, less than or equal to 3)- and (2, less than or equal to 3)-identifying codes are shown to be 1. (C) 2003 Elsevier B.V. All rights reserved.

Mathematics