首页|Algebraic Properties of Powers of Edge Ideals of Vertex-Weighted Oriented Cycles
Algebraic Properties of Powers of Edge Ideals of Vertex-Weighted Oriented Cycles
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Let t be any positive integer and I(Cn)the edge ideal of a vertex-weighted oriented n-cycle graph Cn.We provide explicit formulas for the regularity and depth of I(Cn)t.In particular,we find that the regularity of I(Cn)t is a linear function;Ass(I(Cn)t),the set of associated prime ideals of I(Cn)t,equals Ass(I(Cn));and the depth of I(Cn)t is a constant for all t.We also give some examples to show that these results are related to the direction selection of edges and the weight of vertices.
depthregularitypowers of an idealvertex-weighted oriented cycles
Hong Wang、Guangjun Zhu、Li Xu
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School of Mathematical Sciences,Soochow University Suzhou,Jiangsu 215006,China
Natural Science Foundation of Jiangsu Provincefoundation of the Priority Academic Program Development of Jiangsu Higher Education Institutions.Finally
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