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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 Gi and Hi form a family of non-Sunada twins if Gi and Hi are isospectral of bounded diameter but groups Aut(Gi) and Aut(Hi) are nonisomorphi...

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Main Author: Ustimenko, V.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2020
Series:Algebra and Discrete Mathematics
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/188557
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spelling irk-123456789-1885572023-03-06T01:27:24Z On small world non-Sunada twins and cellular Voronoi diagrams Ustimenko, V. Special infinite families of regular graphs of unbounded degree and of bounded diameter (small world graphs) are considered. Two families of small world graphs Gi and Hi form a family of non-Sunada twins if Gi and Hi are isospectral of bounded diameter but groups Aut(Gi) and Aut(Hi) are nonisomorphic. We say that a family of non-Sunada twins is unbalanced if each Gi is edge-transitive but each Hi is edge-intransitive. If all Gi and Hi 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 Gi is edge-transitive but each Hi is edge-intransitive. We use term edge disbalanced for the family of non-Sunada twins such that all graphs Gi and Hi 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. 2020 Article On small world non-Sunada twins and cellular Voronoi diagrams / V. Ustimenko // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 118–142. — Бібліогр.: 37 назв. — англ. 1726-3255 DOI:10.12958/adm1343 2010 MSC: 05C50, 05C82, 51E24 http://dspace.nbuv.gov.ua/handle/123456789/188557 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
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 Gi and Hi form a family of non-Sunada twins if Gi and Hi are isospectral of bounded diameter but groups Aut(Gi) and Aut(Hi) are nonisomorphic. We say that a family of non-Sunada twins is unbalanced if each Gi is edge-transitive but each Hi is edge-intransitive. If all Gi and Hi 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 Gi is edge-transitive but each Hi is edge-intransitive. We use term edge disbalanced for the family of non-Sunada twins such that all graphs Gi and Hi 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.
format Article
author Ustimenko, V.
spellingShingle Ustimenko, V.
On small world non-Sunada twins and cellular Voronoi diagrams
Algebra and Discrete Mathematics
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
publisher Інститут прикладної математики і механіки НАН України
publishDate 2020
url http://dspace.nbuv.gov.ua/handle/123456789/188557
citation_txt On small world non-Sunada twins and cellular Voronoi diagrams / V. Ustimenko // Algebra and Discrete Mathematics. — 2020. — Vol. 30, № 1. — С. 118–142. — Бібліогр.: 37 назв. — англ.
series Algebra and Discrete Mathematics
work_keys_str_mv AT ustimenkov onsmallworldnonsunadatwinsandcellularvoronoidiagrams
first_indexed 2023-10-18T23:08:38Z
last_indexed 2023-10-18T23:08:38Z
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