Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orthogonal Systems in Finite Graphs   Given a finite graph G there is a corresponding group given by the
presentation with generators the vertices of G and a relation [x,y]=1 for
generators x and y precisely when (x,y) is an edge of G. Such groups are known
as partially commutative groups (or right-angled Artin groups). In this paper
we construct orthogonality theory for graphs with the study of partially
commutative groups in mind. The theory developed here provides tools for the
study of the structure of the centraliser lattice of partially commutative
groups and for their automorphism groups.

32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom