کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4599841 1336825 2013 23 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the critical ideals of graphs
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
On the critical ideals of graphs
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 439, Issue 12, 15 December 2013, Pages 3870–3892
نویسندگان
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