Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Closed Graphs I   A graph is closed when its vertices have a labeling by [n] with a certain
property first discovered in the study of binomial edge ideals. In this
article, we prove that a connected graph has a closed labeling if and only if
it is chordal, claw-free, and has a property we call narrow, which holds when
every vertex is distance at most one from all longest shortest paths of the
graph.

33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an