Details:
Title  On the critical ideals of graphs  Author(s)  Hugo Corrales, Carlos E. Valencia  Type  Article in Journal  Abstract  Abstract 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 Gröbner 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.  Keywords  Critical ideals, Critical group, General Clique number, Cycle, Complete graph  ISSN  00243795 
URL 
http://www.sciencedirect.com/science/article/pii/S0024379513006307 
Language  English  Journal  Linear Algebra and its Applications  Volume  439  Number  12  Pages  3870  3892  Year  2013  Edition  0  Translation 
No  Refereed 
No 
