Extremal digraphs for open neighbourhood location-domination and identifying codes - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Discrete Applied Mathematics Année : 2024

Extremal digraphs for open neighbourhood location-domination and identifying codes

Résumé

A set S of vertices of a digraph D is called an open neighbourhood locating-dominating set if every vertex in D has an in-neighbour in S, and for every pair u, v of vertices of D, there is a vertex in S that is an in-neighbour of exactly one of u and v. The smallest size of an open neighbourhood locating-dominating set of a digraph D is denoted by γOL(D). We study the class of digraphs D whose only open neighbourhood locating-dominating set consists of the whole set of vertices, in other words, γOL(D) is equal to the order of D. We call those digraphs extremal. By considering digraphs with loops allowed, our definition also applies to the related (and more widely studied) concept of identifying codes. We extend previous studies from the literature for both open neighbourhood locating-dominating sets and identifying codes of both undirected and directed graphs. These results all correspond to studying open neighbourhood locating-dominating sets on special classes of digraphs. To do so, we prove general structural properties of extremal digraphs, and we describe how they can all be constructed. We then use these properties to give new proofs of several known results from the literature. We also give a recursive and constructive characterization of the extremal di-trees (digraphs whose underlying undirected graph is a tree).
Fichier principal
Vignette du fichier
Extremal_digraphs_for_OLD_ID_sets.pdf (483.22 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Licence : CC BY NC ND - Paternité - Pas d'utilisation commerciale - Pas de modification

Dates et versions

hal-04398730 , version 1 (16-01-2024)

Licence

Paternité - Pas d'utilisation commerciale - Pas de modification

Identifiants

Citer

Florent Foucaud, Narges Ghareghani, Pouyeh Sharifani. Extremal digraphs for open neighbourhood location-domination and identifying codes. Discrete Applied Mathematics, inPress, 347, pp.62-74. ⟨10.1016/j.dam.2023.12.018⟩. ⟨hal-04398730⟩
27 Consultations
33 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More