Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic Connectivity and Degree Sequences of Trees   We investigate the structure of trees that have minimal algebraic
connectivity among all trees with a given degree sequence. We show that such
trees are caterpillars and that the vertex degrees are non-decreasing on every
path on non-pendant vertices starting at the characteristic set of the Fiedler
vector.

11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol