Minimum Density of Identifying Codes of Hexagonal Grids with a Finite Number of Rows

  • Rudini Sampaio UFC
  • Gabriel A. G. Sobral USP
  • Yoshiko Wakabayashi USP


An identifying code (id code, for short) of a graph is a dominating set such that all vertices have a distinct closed neighbourhood within the code. We present a lower bound for the minimum density of id codes of infinite hexagonal grids with a finite number of rows. We also show that every id code that does not induce a trivial component has density at least 3/7. Finally, we show that when such grids have two rows this minimum density is precisely 9/20. The results on lower bounds are proved using the discharging method.

Palavras-chave: Discharging Method, Hexagonal Grid, Identifying Codes


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SAMPAIO, Rudini; SOBRAL, Gabriel A. G.; WAKABAYASHI, Yoshiko. Minimum Density of Identifying Codes of Hexagonal Grids with a Finite Number of Rows. In: ENCONTRO DE TEORIA DA COMPUTAÇÃO (ETC), 7. , 2022, Niterói. Anais [...]. Porto Alegre: Sociedade Brasileira de Computação, 2022 . p. 145-148. ISSN 2595-6116. DOI: