Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computing the metric dimension of a graph from primary subgraphs   Let $G$ be a connected graph. Given an ordered set $W = \{w_1, w_2,\dots
w_k\}\subseteq V(G)$ and a vertex $u\in V(G)$, the representation of $u$ with
respect to $W$ is the ordered $k$-tuple $(d(u,w_1), d(u,w_2),\dots,$
$d(u,w_k))$, where $d(u,w_i)$ denotes the distance between $u$ and $w_i$. The
set $W$ is a metric generator for $G$ if every two different vertices of $G$
have distinct representations. A minimum cardinality metric generator is called
a \emph{metric basis} of $G$ and its cardinality is called the \emph{metric
dimension} of G. It is well known that the problem of finding the metric
dimension of a graph is NP-Hard. In this paper we obtain closed formulae for
the metric dimension of graphs with cut vertices. The main results are applied
to specific constructions including rooted product graphs, corona product
graphs, block graphs and chains of graphs.

28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th