The directed distance dimension of oriented graphs

Chartrand, Gary, Raines, Michael, and Zhang, Ping. "The directed distance dimension of oriented graphs." Mathematica Bohemica 125.2 (2000): 155-168. <http://eudml.org/doc/248478>.

@article{Chartrand2000,
abstract = {For a vertex $v$ of a connected oriented graph $D$ and an ordered set $W = \lbrace w_1,w_2,\cdots ,w_k\rbrace $ of vertices of $D$, the (directed distance) representation of $v$ with respect to $W$ is the ordered $k$-tuple $r(v\bigm |W) = ( d(v, w_1), d(v, w_2), \cdots , d(v, w_k) )$, where $d(v, w_i)$ is the directed distance from $v$ to $w_i$. The set $W$ is a resolving set for $D$ if every two distinct vertices of $D$ have distinct representations. The minimum cardinality of a resolving set for $D$ is the (directed distance) dimension $\dim (D)$ of $D$. The dimension of a connected oriented graph need not be defined. Those oriented graphs with dimension 1 are characterized. We discuss the problem of determining the largest dimension of an oriented graph with a fixed order. It is shown that if the outdegree of every vertex of a connected oriented graph $D$ of order $n$ is at least 2 and $\dim (D)$ is defined, then $\dim (D) \le n-3$ and this bound is sharp.},
author = {Chartrand, Gary, Raines, Michael, Zhang, Ping},
journal = {Mathematica Bohemica},
keywords = {oriented graphs; directed distance; resolving sets; dimension; oriented graphs; directed distance; resolving sets; dimension},
language = {eng},
number = {2},
pages = {155-168},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The directed distance dimension of oriented graphs},
url = {http://eudml.org/doc/248478},
volume = {125},
year = {2000},
}

TY - JOUR
AU - Chartrand, Gary
AU - Raines, Michael
AU - Zhang, Ping
TI - The directed distance dimension of oriented graphs
JO - Mathematica Bohemica
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 125
IS - 2
SP - 155
EP - 168
AB - For a vertex $v$ of a connected oriented graph $D$ and an ordered set $W = \lbrace w_1,w_2,\cdots ,w_k\rbrace $ of vertices of $D$, the (directed distance) representation of $v$ with respect to $W$ is the ordered $k$-tuple $r(v\bigm |W) = ( d(v, w_1), d(v, w_2), \cdots , d(v, w_k) )$, where $d(v, w_i)$ is the directed distance from $v$ to $w_i$. The set $W$ is a resolving set for $D$ if every two distinct vertices of $D$ have distinct representations. The minimum cardinality of a resolving set for $D$ is the (directed distance) dimension $\dim (D)$ of $D$. The dimension of a connected oriented graph need not be defined. Those oriented graphs with dimension 1 are characterized. We discuss the problem of determining the largest dimension of an oriented graph with a fixed order. It is shown that if the outdegree of every vertex of a connected oriented graph $D$ of order $n$ is at least 2 and $\dim (D)$ is defined, then $\dim (D) \le n-3$ and this bound is sharp.
LA - eng
KW - oriented graphs; directed distance; resolving sets; dimension; oriented graphs; directed distance; resolving sets; dimension
UR - http://eudml.org/doc/248478
ER -