# Sufficient Conditions for a Digraph to Admit A (1, ≤ ℓ)-Identifying Code

@article{Balbuena2021SufficientCF, title={Sufficient Conditions for a Digraph to Admit A (1, ≤ ℓ)-Identifying Code}, author={Camino Balbuena and Cristina Dalf'o and B. Mart'inez-Barona}, journal={Discussiones Mathematicae Graph Theory}, year={2021}, volume={41}, pages={853 - 872} }

Abstract A (1, ≤ ℓ)-identifying code in a digraph D is a subset C of vertices of D such that all distinct subsets of vertices of cardinality at most ℓ have distinct closed in-neighbourhoods within C. In this paper, we give some sufficient conditions for a digraph of minimum in-degree δ− ≥ 1 to admit a (1, ≤ ℓ)-identifying code for ℓ ∈ {δ−, δ− + 1}. As a corollary, we obtain the result by Laihonen that states that a graph of minimum degree δ ≥ 2 and girth at least 7 admits a (1, ≤ δ)-identifying…

## 2 Citations

Characterizing identifying codes from the spectrum of a graph or digraph

- MathematicsLinear Algebra and its Applications
- 2019

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