@article {
author = {Hedetniemi, Jason and Hedetniemi, Stephen and Renu C. Laskar, Renu C. and Mulder, Henry Martyn},
title = {The 2-dimension of a Tree},
journal = {Communications in Combinatorics and Optimization},
volume = {5},
number = {1},
pages = {69-81},
year = {2020},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2019.26495.1119},
abstract = {Let $x$ and $y$ be two distinct vertices in a connected graph $G$. The $x,y$-location of a vertex $w$ is the ordered pair of distances from $w$ to $x$ and $y$, that is, the ordered pair $(d(x,w), d(y,w))$. A set of vertices $W$ in $G$ is $x,y$-located if any two vertices in $W$ have distinct $x,y$-locations. A set $W$ of vertices in $G$ is 2-located if it is $x,y$-located, for some distinct vertices $x$ and $y$. The 2-dimension of $G$ is the order of a largest set that is 2-located in $G$. Note that this notion is related to the metric dimension of a graph, but not identical to it. We study in depth the trees $T$ that have a 2-locating set, that is, have 2-dimension equal to the order of $T$. Using these results, we have a nice characterization of the 2-dimension of arbitrary trees.},
keywords = {resolvability,location number,2-dimension,tree,2-locating set},
url = {http://comb-opt.azaruniv.ac.ir/article_13979.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_13979_67e6ec33d043a864ea37af1094c77ac3.pdf}
}