Sufficient conditions for a digraph to admit a (1,≤ℓ)-identifying code
A (1, ≤ `)-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 ` 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, ≤...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10459.1/66389 |
| Acceso en línea: | https://doi.org/10.7151/dmgt.2218 http://hdl.handle.net/10459.1/66389 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph Digraph Identifying code |
| Sumario: | A (1, ≤ `)-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 ` 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, ≤ `)- identifying code for ` ∈ {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 code. Moreover, we prove that every 1-in-regular digraph has a (1, ≤ 2)-identifying code if and only if the girth of the digraph is at least 5. We also characterize all the 2-in-regular digraphs admitting a (1, ≤ `)-identifying code for ` ∈ {2, 3}. |
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