Brigham, Robert C., et al. "Resolving domination in graphs." Mathematica Bohemica 128.1 (2003): 25-36. <http://eudml.org/doc/249214>.
@article{Brigham2003,
abstract = {For an ordered set $W =\lbrace w_1, w_2, \cdots , w_k\rbrace $ of vertices and a vertex $v$ in a connected graph $G$, the (metric) representation of $v$ with respect to $W$ is the $k$-vector $r(v|W) = (d(v, w_1),d(v, w_2) ,\cdots , d(v, w_k))$, where $d(x,y)$ represents the distance between the vertices $x$ and $y$. The set $W$ is a resolving set for $G$ if distinct vertices of $G$ have distinct representations with respect to $W$. A resolving set of minimum cardinality is called a minimum resolving set or a basis and the cardinality of a basis for $G$ is its dimension $\dim G$. A set $S$ of vertices in $G$ is a dominating set for $G$ if every vertex of $G$ that is not in $S$ is adjacent to some vertex of $S$. The minimum cardinality of a dominating set is the domination number $\gamma (G)$. A set of vertices of a graph $G$ that is both resolving and dominating is a resolving dominating set. The minimum cardinality of a resolving dominating set is called the resolving domination number $\gamma _r(G)$. In this paper, we investigate the relationship among these three parameters.},
author = {Brigham, Robert C., Chartrand, Gary, Dutton, Ronald D., Zhang, Ping},
journal = {Mathematica Bohemica},
keywords = {resolving dominating set; resolving domination number; resolving dominating set; resolving domination number},
language = {eng},
number = {1},
pages = {25-36},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Resolving domination in graphs},
url = {http://eudml.org/doc/249214},
volume = {128},
year = {2003},
}
TY - JOUR
AU - Brigham, Robert C.
AU - Chartrand, Gary
AU - Dutton, Ronald D.
AU - Zhang, Ping
TI - Resolving domination in graphs
JO - Mathematica Bohemica
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 128
IS - 1
SP - 25
EP - 36
AB - For an ordered set $W =\lbrace w_1, w_2, \cdots , w_k\rbrace $ of vertices and a vertex $v$ in a connected graph $G$, the (metric) representation of $v$ with respect to $W$ is the $k$-vector $r(v|W) = (d(v, w_1),d(v, w_2) ,\cdots , d(v, w_k))$, where $d(x,y)$ represents the distance between the vertices $x$ and $y$. The set $W$ is a resolving set for $G$ if distinct vertices of $G$ have distinct representations with respect to $W$. A resolving set of minimum cardinality is called a minimum resolving set or a basis and the cardinality of a basis for $G$ is its dimension $\dim G$. A set $S$ of vertices in $G$ is a dominating set for $G$ if every vertex of $G$ that is not in $S$ is adjacent to some vertex of $S$. The minimum cardinality of a dominating set is the domination number $\gamma (G)$. A set of vertices of a graph $G$ that is both resolving and dominating is a resolving dominating set. The minimum cardinality of a resolving dominating set is called the resolving domination number $\gamma _r(G)$. In this paper, we investigate the relationship among these three parameters.
LA - eng
KW - resolving dominating set; resolving domination number; resolving dominating set; resolving domination number
UR - http://eudml.org/doc/249214
ER -
