A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Progress towards the two-thirds conjecture on locating-total dominating sets
Tekijät: Chakraborty, Dipayan; Foucaud, Florent; Hakanen, Anni; Henning, Michael A.; Wagler, Annegret K.
Kustantaja: Elsevier
Julkaisuvuosi: 2024
Journal: Discrete Mathematics
Tietokannassa oleva lehden nimi: Discrete Mathematics
Artikkelin numero: 114176
Vuosikerta: 347
Numero: 12
ISSN: 0012-365X
eISSN: 1872-681X
DOI: https://doi.org/10.1016/j.disc.2024.114176
Verkko-osoite: https://doi.org/10.1016/j.disc.2024.114176
Rinnakkaistallenteen osoite: https://research.utu.fi/converis/portal/detail/Publication/457313437
Preprintin osoite: https://arxiv.org/abs/2211.14178
Tiivistelmä
We study upper bounds on the size of optimum locating-total dominating sets in graphs. A set S of vertices of a graph G is a locating-total dominating set if every vertex of G has a neighbor in S, and if any two vertices outside S have distinct neighborhoods within S. The smallest size of such a set is denoted by γtL(G). It has been conjectured that γtL(G)≤2n3 holds for every twin-free graph G of order n without isolated vertices. We prove that the conjecture holds for cobipartite graphs, split graphs, block graphs and subcubic graphs.
We study upper bounds on the size of optimum locating-total dominating sets in graphs. A set S of vertices of a graph G is a locating-total dominating set if every vertex of G has a neighbor in S, and if any two vertices outside S have distinct neighborhoods within S. The smallest size of such a set is denoted by γtL(G). It has been conjectured that γtL(G)≤2n3 holds for every twin-free graph G of order n without isolated vertices. We prove that the conjecture holds for cobipartite graphs, split graphs, block graphs and subcubic graphs.
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