| Autor: |
Chakraborty, Dipayan, Foucaud, Florent, Hakanen, Anni, Henning, Michael A., Wagler, Annegret K. |
| Rok vydání: |
2022 |
| Předmět: |
|
| Zdroj: |
Discrete Mathematics 347 (2024), 114176 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1016/j.disc.2024.114176 |
| Popis: |
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 $\gamma^L_t(G)$. It has been conjectured that $\gamma^L_t(G)\leq\frac{2n}{3}$ 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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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