RT journal article
T1 Mixed metric dimension of graphs
A1 Kelenc, Aleksander
A1 Kuziak, Dorota
A1 Taranenko, Andrej
A1 González Yero, Ismael
A2 Estadística e Investigación Operativa
A2 Matemáticas
K1 mixed metric dimension
K1 edge metric dimension
K1 metric dimension
AB Let $G=(V,E)$ be a connected graph. A vertex $w\in V$ distinguishes two elements (vertices or edges) $x,y\in E\cup V$ if $d_G(w,x)\ne d_G(w,y)$. A set $S$ of vertices in a connected graph $G$ is a mixed metric generator for $G$ if every two elements (vertices or edges) of $G$ are distinguished by some vertex of $S$. The smallest cardinality of a mixed metric generator for $G$ is called the mixed metric dimension and is denoted by $\mdim(G)$. In this paper we consider the structure of mixed metric generators and characterize graphs for which the mixed metric dimension equals the trivial lower and upper bounds. We also give results about the mixed metric dimension of some families of graphs and present an upper bound with respect to the girth of a graph. Finally, we prove that the problem of determining the mixed metric dimension of a graph is NP-hard in the general case.
PB Elsevier
SN 0096-3003
YR 2017
FD 2017-12-01
LK http://hdl.handle.net/10498/30889
UL http://hdl.handle.net/10498/30889
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026