Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds on metric dimension for families of planar graphs   The concept of metric dimension has applications in a variety of fields, such
as chemistry, robotic navigation, and combinatorial optimization. We show
bounds for graphs with $n$ vertices and metric dimension $\beta$. For
Hamiltonian outerplanar graphs, we have $\beta \leq
\left\lceil\frac{n}2\right\rceil$; for outerplanar graphs in general, we have
$\beta \leq \left\lfloor\frac{2n}{3}\right\rfloor$; for maximal planar graphs,
we have $\beta \leq \left\lfloor\frac{3n}{4}\right\rfloor$. We also show that
bipyramids have a metric dimension of $\left\lfloor\frac{2n}{5}\right\rfloor +
1$. It is conjectured that the metric dimension of maximal planar graphs in
general is on the order of $\left\lfloor\frac{2n}{5}\right\rfloor$.

27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio