Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cographs   Cographs--defined most simply as complete graphs with colored lines--both
dualize and generalize ordinary graphs, and promise a comparably wide range of
applications. This article introduces them by examples, catalogues, and
elementary properties. Any finite cograph may be realized in several ways,
including inner products, polynomials, geometrically, or by "fat
intersections." Particular classes then considered include sum cographs (points
in Z or Zn; the line C(P,Q) joining points P and Q defined C(P,Q) = P+Q);
difference cographs (C(P,Q) = |P-Q|; and intersection cographs (points are
sets; C(P,Q) = P intersect Q). Intersection cographs, especially, promise many
applications; described here are some to aesthetics. Point-line cographs turn
out equivalent to linear spaces. Finally solved here is an interesting
group-theoretic problem arising from group cographs (points in a group; C(P,Q)
= {PQ,QP}).

20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph