Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The maximal tree with respect to the exponential of the second Zagreb
  index   The second Zagreb index is $M_2(G)=\sum_{uv\in E(G)}d_{G}(u)d_{G}(v)$. It was
found to occur in certain approximate expressions of the total $\pi$-electron
energy of alternant hydrocarbons and used by various researchers in their QSPR
and QSAR studies. Recently the exponential of a vertex-degree-based topological
index was introduced. It is known that among all trees with $n$ vertices, the
exponential of the second Zagreb index $e^{M_2}$ attains its minimum value in
the path $P_n$. In this paper, we show that $e^{M_2}$ attains its maximum value
in the balanced double star with $n$ vertices and solve an open problem
proposed by Cruz and Rada [R. Cruz, J. Rada, The path and the star as extremal
values of vertex-degree-based topological indices among trees, MATCH Commun.
Math. Comput. Chem. 82 (3) (2019) 715-732].

12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an