Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Twins and Vertex- Identification on Graphs   Recently, several vertex identifying notions were introduced (identifying
coloring, lid-coloring, ...), these notions were inspired by identifying codes.
All of them, as well as original identifying code, are based on separating two
vertices according to some conditions on their closed neighborhood. Therefore,
twins can not be identified. So most of known results focus on twin-free graph.
Here, we show how twins can modify optimal value of vertex-identifying
parameters for identifying coloring and locally identifying coloring.
  \textbf{Keyword :}
  Identifying coloring, locally identifying coloring, twins, separating.

25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: solv-int
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th