Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locating domination in bipartite graphs and their complements   A set $S$ of vertices of a graph $G$ is \emph{distinguishing} if the sets of
neighbors in $S$ for every pair of vertices not in $S$ are distinct. A
\emph{locating-dominating set} of $G$ is a dominating distinguishing set. The
\emph{location-domination number} of $G$, $\lambda(G)$, is the minimum
cardinality of a locating-dominating set. In this work we study relationships
between $\lambda({G})$ and $\lambda (\overline{G})$ for bipartite graphs. The
main result is the characterization of all connected bipartite graphs $G$
satisfying $\lambda (\overline{G})=\lambda({G})+1$. To this aim, we define an
edge-labeled graph $G^S$ associated with a distinguishing set $S$ that turns
out to be very helpful.

14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys