Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On complexity and Jacobian of cone over a graph   For any given graph $G$ consider a graph $\widetilde{G}$ which is a cone over
graph $G.$ In this paper, we study two important invariants of such a cone.
Namely, complexity (the number of spanning trees) and the Jacobian of a graph.
We prove that complexity of graph $\widetilde{G}$ coincides the number of
rooted spanning forests in graph $G$ and the Jacobian of $\widetilde{G}$ is
isomorphic to cokernel of the operator $I+L(G),$ where $L(G)$ is Laplacian of
$G$ and $I$ is the identity matrix. As a consequence, one can calculate the
complexity of $\widetilde{G}$ as $\det(I+L(G)).$

23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an