On small world non-Sunada twins and cellular Voronoi diagrams

On small world non-Sunada twins and cellular Voronoi diagrams

Special infinite families of regular graphs of unbounded degree and of bounded diameter (small world graphs) are considered. Two families of small world graphs \(G_i\) and \(H_i\) form a family of non-Sunada twins if \(G_i\) and \(H_i\) are isospectral of bounded diameter but groups \(Aut(G_i)\) and...

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Bibliographic Details
Date:2020
Main Author: Ustimenko, V.
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2020
Subjects:
Laplacians
isospectral graphs
small world graphs
distance-regular graphs
non-Sunada constructions
graph Voronoi diagram
thin Voronoi cells
05C50
05C82
51E24
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1343
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id admjournalluguniveduua-article-1343
record_format ojs
spelling admjournalluguniveduua-article-13432021-01-04T06:21:31Z On small world non-Sunada twins and cellular Voronoi diagrams Ustimenko, V. Laplacians, isospectral graphs, small world graphs, distance-regular graphs, non-Sunada constructions, graph Voronoi diagram, thin Voronoi cells 05C50, 05C82, 51E24 Special infinite families of regular graphs of unbounded degree and of bounded diameter (small world graphs) are considered. Two families of small world graphs \(G_i\) and \(H_i\) form a family of non-Sunada twins if \(G_i\) and \(H_i\) are isospectral of bounded diameter but groups \(Aut(G_i)\) and \(Aut(H_i)\) are nonisomorphic.We say that a family of non-Sunada twins is unbalanced if each \(G_i\) is edge-transitive but each \(H_i\) is edge-intransitive. If all \(G_i\) and \(H_i\) are edge-transitive we have a balanced family of small world non-Sunada twins. We say that a family of non-Sunada twins is strongly unbalanced if each \(G_i\) is edge-transitive but each \(H_i\) is edge-intransitive.We use term edge disbalanced for the family of non-Sunada twins such that all graphs \(G_i\) and \(H_i\) are edge-intransitive. We present explicit constructions of the above defined families. Two new families of distance-regular—but not distance-transitive—graphs will be introduced. Lugansk National Taras Shevchenko University University of Maria Curie-Sklodowska Institute of telecommunication and Global Information Space, Ukraine 2020-12-30 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1343 10.12958/adm1343 Algebra and Discrete Mathematics; Vol 30, No 1 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1343/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1343/501 Copyright (c) 2020 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2021-01-04T06:21:31Z
collection OJS
language English
topic Laplacians
isospectral graphs
small world graphs
distance-regular graphs
non-Sunada constructions
graph Voronoi diagram
thin Voronoi cells
05C50
05C82
51E24
spellingShingle Laplacians
isospectral graphs
small world graphs
distance-regular graphs
non-Sunada constructions
graph Voronoi diagram
thin Voronoi cells
05C50
05C82
51E24
Ustimenko, V.
On small world non-Sunada twins and cellular Voronoi diagrams
topic_facet Laplacians
isospectral graphs
small world graphs
distance-regular graphs
non-Sunada constructions
graph Voronoi diagram
thin Voronoi cells
05C50
05C82
51E24
format Article
author Ustimenko, V.
author_facet Ustimenko, V.
author_sort Ustimenko, V.
title On small world non-Sunada twins and cellular Voronoi diagrams
title_short On small world non-Sunada twins and cellular Voronoi diagrams
title_full On small world non-Sunada twins and cellular Voronoi diagrams
title_fullStr On small world non-Sunada twins and cellular Voronoi diagrams
title_full_unstemmed On small world non-Sunada twins and cellular Voronoi diagrams
title_sort on small world non-sunada twins and cellular voronoi diagrams
description Special infinite families of regular graphs of unbounded degree and of bounded diameter (small world graphs) are considered. Two families of small world graphs \(G_i\) and \(H_i\) form a family of non-Sunada twins if \(G_i\) and \(H_i\) are isospectral of bounded diameter but groups \(Aut(G_i)\) and \(Aut(H_i)\) are nonisomorphic.We say that a family of non-Sunada twins is unbalanced if each \(G_i\) is edge-transitive but each \(H_i\) is edge-intransitive. If all \(G_i\) and \(H_i\) are edge-transitive we have a balanced family of small world non-Sunada twins. We say that a family of non-Sunada twins is strongly unbalanced if each \(G_i\) is edge-transitive but each \(H_i\) is edge-intransitive.We use term edge disbalanced for the family of non-Sunada twins such that all graphs \(G_i\) and \(H_i\) are edge-intransitive. We present explicit constructions of the above defined families. Two new families of distance-regular—but not distance-transitive—graphs will be introduced.
publisher Lugansk National Taras Shevchenko University
publishDate 2020
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1343
work_keys_str_mv AT ustimenkov onsmallworldnonsunadatwinsandcellularvoronoidiagrams
first_indexed 2025-12-02T15:42:07Z
last_indexed 2025-12-02T15:42:07Z
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