On the critical ideals of graphs

Hugo Corrales, Carlos E. Valencia

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

17 Citas (Scopus)

Resumen

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.

Idioma originalInglés
Páginas (desde-hasta)3870-3892
Número de páginas23
PublicaciónLinear Algebra and Its Applications
Volumen439
N.º12
DOI
EstadoPublicada - 15 dic 2013
Publicado de forma externa

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