Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Stronger Types of Locating-dominating Codes   Locating-dominating codes in a graph find their application in sensor
networks and have been studied extensively over the years. A
locating-dominating code can locate one object in a sensor network, but if
there is more than one object, it may lead to false conclusions. In this paper,
we consider stronger types of locating-dominating codes which can locate one
object and detect if there are multiple objects. We study the properties of
these codes and provide bounds on the smallest possible size of these codes,
for example, with the aid of the Dilworth number and Sperner families.
Moreover, these codes are studied in trees and Cartesian products of graphs. We
also give the complete realization theorems for the coexistence of the smallest
possible size of these codes and the optimal locating-dominating codes in a
graph.

5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph