Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A connection between the bipartite complements of line graphs and the
  line graphs with two positive eigenvalues   In 1974 Cvetkovi\'c and Simi\'c showed which graphs $G$ are the bipartite
complements of line graphs. In 2002 Borovi\'canin showed which line graphs
$L(H)$ have third largest eigenvalue $\lambda_3\leq0$. Our first observation is
that two of the graphs Borovi\'canin found are the complements of two of the
graphs found by Cvetkovi\'c and Simi\'c. Using the Courant-Weyl inequalities we
show why this is and reprove the result of Borovi\'canin, highlighting some
features of the graphs found by both.

30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs