RT journal article
T1 On the strong metric dimension of Cartesian and direct products of graphs
A1 Rodríguez Velázquez, Juan A.
A1 González Yero, Ismael
A1 Kuziak, Dorota
A1 Oellermann, Ortrud
A2 Estadística e Investigación Operativa
A2 Matemáticas
K1 Strong resolving set
K1 strong metric dimension
K1 Cartesian product of graphs
K1 direct product of graphs
K1 strong resolving graph
AB Let $G$ be a connected graph. A vertex $w$ {\em strongly resolves} a pair $u, v$ of vertices of $G$ if there exists some shortest$u-w$ path containing $v$ or some shortest $v-w$ path containing $u$. A set $W$ of vertices is a {\em strong resolving set} for $G$ if every pair ofvertices of $G$ is strongly resolved by some vertex of $W$. The smallest cardinality of a strong resolving set for $G$ is called the {\em strong metric dimension} of $G$. It is known  that the problem of computing the strong metricdimension of a graph is NP-hard. In this paper we obtain closed formulae for the strong metric dimension of several families of the Cartesian product of graphs and the direct product of graphs.
PB Elsevier
SN 0012-365X
YR 2014
FD 2014-11-28
LK http://hdl.handle.net/10498/30926
UL http://hdl.handle.net/10498/30926
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026