Depth and Stanley depth of the edge ideals of the strong product of some graphs

被引：5

作者：

Iqbal, Zahid ^{[1
]}

Ishaq, Muhammad ^{[1
]}

Binyamin, Muhammad Ahsan ^{[2
]}

机构：

[1] Natl Univ Sci & Technol, Sch Nat Sci, Sect H-12, Islamabad 44000, Pakistan

[2] Govt Coll Univ Faisalabad, Dept Math, Faisalabad, Pakistan

来源：

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS | 2021年 / 50卷 / 01期

关键词：

depth; Stanley depth; Stanley decomposition; monomial ideal; edge ideal; strong product of graphs;

D O I：

10.15672/hujms.638033

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study depth and Stanley depth of the edge ideals and quotient rings of the edge ideals, associated with classes of graphs obtained by the strong product of two graphs. We consider the cases when either both graphs are arbitrary paths or one is an arbitrary path and the other is an arbitrary cycle. We give exact formula for values of depth and Stanley depth for some subclasses. We also give some sharp upper bounds for depth and Stanley depth in the general cases.

引用

页码：92 / 109

页数：18

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