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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
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