Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: General sum-connectivity index of trees and unicyclic graphs with fixed
  maximum degree   The general sum-connectivity index of a graph $G$ is defined as
$\chi_\alpha(G)=\sum\limits_{uv\in E(G)} {(d(u)+d(v))^{\alpha}}$, where $d(v)$
denotes the degree of the vertex $v$ in $G$ and $\alpha$ is a real number. In
this paper it is deduced the maximum value for the general sum-connectivity
index of $n$-vertex trees for $-1.7036\leq \alpha <0$ and of $n$-vertex
unicyclic graphs for $-1\le \alpha <0$ respectively, with fixed maximum degree
$\triangle $. The corresponding extremal graphs, as well as the $n$-vertex
unicyclic graphs with the second maximum general sum-connectivity index for
$n\ge 4$ are characterized. This extends the corresponding results by Du, Zhou
and Trinajsti\' c [arXiv:1210.5043] about sum-connectivity index.

11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph