IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i20p3785-d941777.html
   My bibliography  Save this article

Experimental Investigation of the Generalized Euler Characteristic of the Networks Split at Edges

Author

Listed:
  • Omer Farooq

    (Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland)

  • Afshin Akhshani

    (Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland)

  • Małgorzata Białous

    (Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland)

  • Szymon Bauch

    (Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland)

  • Michał Ławniczak

    (Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland)

  • Leszek Sirko

    (Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland)

Abstract

We discuss a connection between the generalized Euler characteristic E o ( | V D o | ) of the original graph which was split at edges into two separate subgraphs and their generalized Euler characteristics E i ( | V D i | ) , i = 1 , 2 , where | V D o | and | V D i | are the numbers of vertices with the Dirichlet boundary conditions in the graphs. Applying microwave networks which simulate quantum graphs, we show that the experimental determination of the generalized Euler characteristics E o ( | V D o | ) and E i ( | V D i | ) , i = 1 , 2 allows finding the number of edges in which the subnetworks were connected.

Suggested Citation

  • Omer Farooq & Afshin Akhshani & Małgorzata Białous & Szymon Bauch & Michał Ławniczak & Leszek Sirko, 2022. "Experimental Investigation of the Generalized Euler Characteristic of the Networks Split at Edges," Mathematics, MDPI, vol. 10(20), pages 1-10, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3785-:d:941777
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/20/3785/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/20/3785/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3785-:d:941777. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.