Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimizing Laplacian spectral radius of unicyclic graphs with fixed
  girth   In this paper we consider the following problem: Over the class of all simple
connected unicyclic graphs on $n$ vertices with girth $g$ ($n,g$ being fixed),
which graph minimizes the Laplacian spectral radius? We prove that the graph
$U_{n,g}$ (defined in Section 1) uniquely minimizes the Laplacian spectral
radius for $n\geq 2g-1$ when $g$ is even and for $n\geq 3g-1$ when $g$ is odd.

3
The categories of this paper are: physics
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an