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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Bibliographic Details
Published in:Journal of mathematics (Hidawi) 2022, Vol.2022 (1)
Main Authors: Zeng, Guiling, Munir, Muhammad Mobeen, Farooki, Raheel, Athar, Muhammad, Liu, Jia Bao
Format: Article
Language:English
Subjects:
Algebra
Circuits
Decomposition
Graph theory
Graphs
Invariants
Mathematics
Modules
Network analysis
Quotients
Variables
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Summary: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.
ISSN:2314-4629
2314-4785
DOI:10.1155/2022/9706112