English

Characterizing extremal digraphs for identifying codes and extremal cases of Bondy's theorem on induced subsets

Discrete Mathematics 2013-10-11 v3 Combinatorics

Abstract

An identifying code of a (di)graph GG is a dominating subset CC of the vertices of GG such that all distinct vertices of GG have distinct (in)neighbourhoods within CC. In this paper, we classify all finite digraphs which only admit their whole vertex set in any identifying code. We also classify all such infinite oriented graphs. Furthermore, by relating this concept to a well known theorem of A. Bondy on set systems we classify the extremal cases for this theorem.

Keywords

Cite

@article{arxiv.1010.2985,
  title  = {Characterizing extremal digraphs for identifying codes and extremal cases of Bondy's theorem on induced subsets},
  author = {Florent Foucaud and Reza Naserasr and Aline Parreau},
  journal= {arXiv preprint arXiv:1010.2985},
  year   = {2013}
}