Stanley Depth of the Edge Ideal of Extended Gear Networks and Application in Circuit Analysis
Graph theory is widely used in power network analysis, complex network, and engineering calculation. Stanley depth is a geometric invariant of the module which is closely related to an algebraic invariant called depth of the module. At first, we propose a generalization of classical gear graph and e...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/9706112 |
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| _version_ | 1832553697467432960 |
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| author | Guiling Zeng Muhammad Mobeen Munir Raheel Farooki Muhammad Athar Jia Bao Liu |
| author_facet | Guiling Zeng Muhammad Mobeen Munir Raheel Farooki Muhammad Athar Jia Bao Liu |
| author_sort | Guiling Zeng |
| collection | DOAJ |
| description | Graph theory is widely used in power network analysis, complex network, and engineering calculation. Stanley depth is a geometric invariant of the module which is closely related to an algebraic invariant called depth of the module. At first, we propose a generalization of classical gear graph and extended m−level gear graph and then establish general closed formulas for the sharp bounds of Stanley depth of quotient of edge ideals associated to extended m-level gear graph. We establish general closed formulas for the sharp bounds of Stanley depth of quotient of edge ideals associated to extended gear graph. We recover these bounds for Stanley depth of the quotient of edge ideals associated to classical gear graphs. |
| format | Article |
| id | doaj-art-911bf2fe15404861b7f656da541c6823 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-911bf2fe15404861b7f656da541c68232025-02-03T05:53:29ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/9706112Stanley Depth of the Edge Ideal of Extended Gear Networks and Application in Circuit AnalysisGuiling Zeng0Muhammad Mobeen Munir1Raheel Farooki2Muhammad Athar3Jia Bao Liu4Department of Electrical and AutomationDepartment of MathematicsAbdus Salam School of MathematicsDepartment of Mathematics, Division of Science and TechnologySchool of Mathematics and PhysicsGraph theory is widely used in power network analysis, complex network, and engineering calculation. Stanley depth is a geometric invariant of the module which is closely related to an algebraic invariant called depth of the module. At first, we propose a generalization of classical gear graph and extended m−level gear graph and then establish general closed formulas for the sharp bounds of Stanley depth of quotient of edge ideals associated to extended m-level gear graph. We establish general closed formulas for the sharp bounds of Stanley depth of quotient of edge ideals associated to extended gear graph. We recover these bounds for Stanley depth of the quotient of edge ideals associated to classical gear graphs.http://dx.doi.org/10.1155/2022/9706112 |
| spellingShingle | Guiling Zeng Muhammad Mobeen Munir Raheel Farooki Muhammad Athar Jia Bao Liu Stanley Depth of the Edge Ideal of Extended Gear Networks and Application in Circuit Analysis Journal of Mathematics |
| title | Stanley Depth of the Edge Ideal of Extended Gear Networks and Application in Circuit Analysis |
| title_full | Stanley Depth of the Edge Ideal of Extended Gear Networks and Application in Circuit Analysis |
| title_fullStr | Stanley Depth of the Edge Ideal of Extended Gear Networks and Application in Circuit Analysis |
| title_full_unstemmed | Stanley Depth of the Edge Ideal of Extended Gear Networks and Application in Circuit Analysis |
| title_short | Stanley Depth of the Edge Ideal of Extended Gear Networks and Application in Circuit Analysis |
| title_sort | stanley depth of the edge ideal of extended gear networks and application in circuit analysis |
| url | http://dx.doi.org/10.1155/2022/9706112 |
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