Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp bounds on the $A_{\alpha}$-index of graphs in terms of the
  independence number   Given a graph $G$, the adjacency matrix and degree diagonal matrix of $G$ are
denoted by $A(G)$ and $D(G)$, respectively. In 2017, Nikiforov \cite{0007}
proposed the $A_{\alpha}$-matrix: $A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G),$
where $\alpha\in [0, 1]$. The largest eigenvalue of this novel matrix is called
the $A_\alpha$-index of $G$. In this paper, we characterize the graphs with
minimum $A_\alpha$-index among $n$-vertex graphs with independence number $i$
for $\alpha\in[0,1)$, where
$i=1,\lfloor\frac{n}{2}\rfloor,\lceil\frac{n}{2}\rceil,{\lfloor\frac{n}{2}\rfloor+1},n-3,n-2,n-1,$
whereas for $i=2$ we consider the same problem for $\alpha\in
[0,\frac{3}{4}{]}.$ Furthermore, we determine the unique graph (resp. tree) on
$n$ vertices with given independence number having the maximum $A_\alpha$-index
with $\alpha\in[0,1)$, whereas for the $n$-vertex bipartite graphs with given
independence number, we characterize the unique graph having the maximum
$A_\alpha$-index with $\alpha\in[\frac{1}{2},1).$

16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex