Characterizing extremal graphs for open neighbourhood location-domination - Université Clermont Auvergne Accéder directement au contenu
Article Dans Une Revue Discrete Applied Mathematics Année : 2021

Characterizing extremal graphs for open neighbourhood location-domination

Résumé

An open neighbourhood locating-dominating set is a set S of vertices of a graph G such that each vertex of G has a neighbour in S, and for any two vertices u, v of G, there is at least one vertex in S that is a neighbour of exactly one of u and v. We characterize those graphs whose only open neighbourhood locating-dominating set is the whole set of vertices. More precisely, we prove that these graphs are exactly the graphs for which all connected components are half-graphs (a half-graph is a special bipartite graph with both parts of the same size, where each part can be ordered so that the open neighbourhoods of consecutive vertices differ by exactly one vertex). This corrects a wrong characterization from the literature.
Fichier principal
Vignette du fichier
Open_Neighborhood_Locating_Dominating_Set_on_Undirected_Graphs.pdf (315.95 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03540625 , version 1 (24-01-2022)

Identifiants

Citer

Florent Foucaud, Narges Ghareghani, Aida Roshany-Tabrizi, Pouyeh Sharifani. Characterizing extremal graphs for open neighbourhood location-domination. Discrete Applied Mathematics, 2021, 302, pp.76-79. ⟨10.1016/j.dam.2021.06.006⟩. ⟨hal-03540625⟩
27 Consultations
22 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More