Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On graphs with exactly two positive eigenvalues   The inertia of a graph $G$ is defined to be the triplet $In(G) = (p(G), n(G),
$ $\eta(G))$, where $p(G)$, $n(G)$ and $\eta(G)$ are the numbers of positive,
negative and zero eigenvalues (including multiplicities) of the adjacency
matrix $A(G)$, respectively. Traditionally $p(G)$ (resp. $n(G)$) is called the
positive (resp. negative) inertia index of $G$. In this paper, we introduce
three types of congruent transformations for graphs that keep the positive
inertia index and negative inertia index. By using these congruent
transformations, we determine all graphs with exactly two positive eigenvalues
and one zero eigenvalue.

16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin