Stanley Depth of the Edge Ideal of Extended Gear Networks and Application in Circuit Analysis. (6th June 2022)

• Record Type: Journal Article
• Authors: Zeng, Guiling; Munir, Muhammad Mobeen; Farooki, Raheel; Athar, Muhammad; Liu, Jia Bao
• Other Names: Tartarone Francesca Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2022(2022)
• Publication Date: 2022-06-06
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2022/9706112
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : 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.