TY - JOUR
ID - 13979
TI - The 2-dimension of a Tree
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Hedetniemi, Jason
AU - Hedetniemi, Stephen
AU - Renu C. Laskar, Renu C.
AU - Mulder, Henry Martyn
AD - Department of Mathematics
Wingate University
Wingate NC
USA
AD - School of Computing
Clemson University
Clemson, SC
U.S.A.
AD - Clemson University
AD - Econometrisch Instituut
Erasmus Universiteit
Rotterdam
Netherlands
Y1 - 2020
PY - 2020
VL - 5
IS - 1
SP - 69
EP - 81
KW - resolvability
KW - location number
KW - 2-dimension
KW - tree
KW - 2-locating set
DO - 10.22049/cco.2019.26495.1119
N2 - 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.
UR - http://comb-opt.azaruniv.ac.ir/article_13979.html
L1 - http://comb-opt.azaruniv.ac.ir/article_13979_67e6ec33d043a864ea37af1094c77ac3.pdf
ER -