Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A golden ratio inequality for vertex degrees of graphs   Motivated by the study of the crossing number of graphs, it is shown that,
for trees, the sum of the products of the degrees of the end-vertices of all
edges has an upper bound in terms of the sum of all vertex degrees to the power
of $\phi^2$, where $\phi$ is the golden ratio. The exponent $\phi^2$ is best
possible. This inequality is generalized for all graphs with bounded maximum
average degree.

27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs