Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the critical ideals of graphs   We introduce some determinantal ideals of the generalized Laplacian matrix
associated to a digraph G, that we call critical ideals of G. Critical ideals
generalize the critical group and the characteristic polynomials of the
adjacency and Laplacian matrices of a digraph. The main results of this article
are the determination of some minimal generator sets and the reduced Grobner
basis for the critical ideals of the complete graphs, the cycles and the paths.
Also, we establish a bound between the number of trivial critical ideals and
the stability and clique numbers of a graph.

28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph