Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Metric Dimension of Infinite Graphs   A set of vertices $S$ \emph{resolves} a graph $G$ if every vertex is uniquely
determined by its vector of distances to the vertices in $S$. The \emph{metric
dimension} of a graph $G$ is the minimum cardinality of a resolving set. In
this paper we study the metric dimension of infinite graphs such that all its
vertices have finite degree. We give necessary conditions for those graphs to
have finite metric dimension and characterize infinite trees with finite metric
dimension. We also establish some results about the metric dimension of the
cartesian product of finite and infinite graphs, and give the metric dimension
of the cartesian product of several families of graphs.

24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat