English

Small clique number graphs with three trivial critical ideals

Combinatorics 2013-11-26 v1 Commutative Algebra

Abstract

The critical ideals of a graph are the determinantal ideals of the generalized Laplacian matrix associated to a graph. In this article we provide a set of minimal forbidden graphs for the set of graphs with at most three trivial critical ideals. Then we use these forbidden graphs to characterize the graphs with at most three trivial critical ideals and clique number equal to 2 and 3.

Keywords

Cite

@article{arxiv.1311.5927,
  title  = {Small clique number graphs with three trivial critical ideals},
  author = {Carlos A. Alfaro and Carlos E. Valencia},
  journal= {arXiv preprint arXiv:1311.5927},
  year   = {2013}
}

Comments

33 pages, 3 figures