The Generalized Euler Characteristics of the Graphs Split at Vertices

We show that there is a relationship between the generalized Euler characteristic [Formula: see text] of the original graph that was split at vertices into two disconnected subgraphs [Formula: see text] and their generalized Euler characteristics [Formula: see text]. Here, [Formula: see text] and [F...

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Autores principales: Farooq, Omer, Ławniczak, Michał, Akhshani, Afshin, Bauch, Szymon, Sirko, Leszek
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8947457/
https://www.ncbi.nlm.nih.gov/pubmed/35327898
http://dx.doi.org/10.3390/e24030387
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author Farooq, Omer
Ławniczak, Michał
Akhshani, Afshin
Bauch, Szymon
Sirko, Leszek
author_facet Farooq, Omer
Ławniczak, Michał
Akhshani, Afshin
Bauch, Szymon
Sirko, Leszek
author_sort Farooq, Omer
collection PubMed
description We show that there is a relationship between the generalized Euler characteristic [Formula: see text] of the original graph that was split at vertices into two disconnected subgraphs [Formula: see text] and their generalized Euler characteristics [Formula: see text]. Here, [Formula: see text] and [Formula: see text] denote the numbers of vertices with the Dirichlet boundary conditions in the graphs. The theoretical results are experimentally verified using microwave networks that simulate quantum graphs. We demonstrate that the evaluation of the generalized Euler characteristics [Formula: see text] and [Formula: see text] allow us to determine the number of vertices where the two subgraphs were initially connected.
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spelling pubmed-89474572022-03-25 The Generalized Euler Characteristics of the Graphs Split at Vertices Farooq, Omer Ławniczak, Michał Akhshani, Afshin Bauch, Szymon Sirko, Leszek Entropy (Basel) Article We show that there is a relationship between the generalized Euler characteristic [Formula: see text] of the original graph that was split at vertices into two disconnected subgraphs [Formula: see text] and their generalized Euler characteristics [Formula: see text]. Here, [Formula: see text] and [Formula: see text] denote the numbers of vertices with the Dirichlet boundary conditions in the graphs. The theoretical results are experimentally verified using microwave networks that simulate quantum graphs. We demonstrate that the evaluation of the generalized Euler characteristics [Formula: see text] and [Formula: see text] allow us to determine the number of vertices where the two subgraphs were initially connected. MDPI 2022-03-09 /pmc/articles/PMC8947457/ /pubmed/35327898 http://dx.doi.org/10.3390/e24030387 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Farooq, Omer
Ławniczak, Michał
Akhshani, Afshin
Bauch, Szymon
Sirko, Leszek
The Generalized Euler Characteristics of the Graphs Split at Vertices
title The Generalized Euler Characteristics of the Graphs Split at Vertices
title_full The Generalized Euler Characteristics of the Graphs Split at Vertices
title_fullStr The Generalized Euler Characteristics of the Graphs Split at Vertices
title_full_unstemmed The Generalized Euler Characteristics of the Graphs Split at Vertices
title_short The Generalized Euler Characteristics of the Graphs Split at Vertices
title_sort generalized euler characteristics of the graphs split at vertices
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8947457/
https://www.ncbi.nlm.nih.gov/pubmed/35327898
http://dx.doi.org/10.3390/e24030387
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