On the Critical Ideals of Complete Multipartite Graphs
Yibo Gao · Electronic Journal of Linear Algebra · 2020
The notions of critical ideals and characteristic ideals of graphs are introduced by Corrales and Valencia to study properties of graphs, including clique number, zero forcing number, minimum rank and critical group. In this paper, we provide methods to compute critical ideals of complete multipartite graphs and obtain complete answers for the characteristic ideals of complete multipartite graphs.