Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The asymptotic value of graph energy for random graphs with degree-based
  weights   In this paper, we investigate the energy of a weighted random graph $G_p(f)$
in $G_{n,p}(f)$, in which each edge $ij$ takes the weight $f(d_i,d_j)$, where
$d_v$ is a random variable, the degree of vertex $v$ in the random graph $G_p$
of the Erd\"{o}s--R\'{e}nyi random graph model $G_{n,p}$, and $f$ is a
symmetric real function on two variables. Suppose $|f(d_i,d_j)|\leq C n^m$ for
some constants $C, m>0$, and $f((1+o(1))np,(1+o(1))np)=(1+o(1))f(np,np)$. Then,
for almost all graphs $G_p(f)$ in $G_{n,p}(f)$, the energy of $G_p(f)$ is
$(1+o(1))f(np,np)\frac{8}{3\pi}\sqrt{p(1-p)}\cdot n^{3/2},$ where $p\in(0,1)$
is any fixed and independent of $n$. Consequently, with this one basket we can
get the asymptotic values of various kinds of graph energies of chemical use,
such as Randi\'c energy, ABC energy, and energies of random matrices obtained
from various kinds of degree-based chemical indices.

22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga