Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eigenvalue location in cographs   We give an $O(n)$ time and space algorithm for constructing a diagonal matrix
congruent to A+xI, where A is the adjacency matrix of a cograph and $x\in
\mathbb{R}$. Applications include determining the number of eigenvalues of a
cograph's adjacency matrix that lie in any interval, obtaining a formula for
the inertia of a cograph, and exhibiting infinitely many pairs of equienergetic
cographs with integer energy.

30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex