Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maxima of the $Q$-index for outer-planar graphs   The $Q$-$index$ of graph $G$ is the largest eigenvalue $q(G)$ of its signless
Laplacian $Q(G)$. In this paper, we prove that the graph $K_{1}\nabla P_{n-1}$
has the maximal $Q$-index among all outer-planar graphs of order $n$.

24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph