Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal resolving sets for the hypercube   For a given undirected graph $G$, an \emph{ordered} subset $S =
{s_1,s_2,...,s_k} \subseteq V$ of vertices is a resolving set for the graph if
the vertices of the graph are distinguishable by their vector of distances to
the vertices in $S$. While a superset of any resolving set is always a
resolving set, a proper subset of a resolving set is not necessarily a
resolving set, and we are interested in determining resolving sets that are
minimal or that are minimum (of minimal cardinality). Let $Q^n$ denote the
$n$-dimensional hypercube with vertex set ${0,1}^n$. In Erd\"os and Renyi
(Erdos & Renyi, 1963) it was shown that a particular set of $n$ vertices forms
a resolving set for the hypercube. The main purpose of this note is to prove
that a proper subset of that set of size $n-1$ is also a resolving set for the
hypercube for all $n \ge 5$ and that this proper subset is a minimal resolving
set.

28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat