Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Realizability problem for commuting graphs   We investigate properties which ensure that a given finite graph is the
commuting graph of a group or semigroup. We show that all graphs on at least
two vertices such that no vertex is adjacent to all other vertices is the
commuting graph of some semigroup. Moreover, we obtain a complete
classification of the graphs with an isolated vertex or edge that are the
commuting graph of a group and the cycles that are the commuting graph of a
centrefree semigroup.

22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org