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

Omer Farooq (), Afshin Akhshani, Małgorzata Białous, Szymon Bauch, Michał Ławniczak () and Leszek Sirko ()
Additional contact information
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

Mathematics, 2022, vol. 10, issue 20, 1-10

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.

Keywords: microwave networks; quantum graphs; Euler characteristic; Neumann and Dirichlet boundary conditions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/20/3785/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/20/3785/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:20:p:3785-:d:941777

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().