Digraphs with at most one trivial critical ideal
Combinatorics
2017-03-28 v1
Abstract
Critical ideals generalize the critical group, Smith group and the characteristic polynomials of the adjacency and Laplacian matrices of a graph. We give a complete characterization of the digraphs with at most one trivial critical ideal. Which implies the characterizations of the digraphs whose critical group has one invariant factor equal to one, and the digraphs whose Smith group has one invariant factor equal to one.
Keywords
Cite
@article{arxiv.1703.08621,
title = {Digraphs with at most one trivial critical ideal},
author = {Carlos A. Alfaro and Carlos E. Valencia and Adrián Vázquez-Ávila},
journal= {arXiv preprint arXiv:1703.08621},
year = {2017}
}
Comments
12 pages, 4 figures