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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188557 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862582407749697536 |
|---|---|
| author | Ustimenko, V. |
| author_facet | Ustimenko, V. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-11-26T23:06:16Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-188557 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-26T23:06:16Z |
| publishDate | 2020 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Ustimenko, V. 2023-03-05T17:37:27Z 2023-03-05T17:37:27Z 2020 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 https://nasplib.isofts.kiev.ua/handle/123456789/188557 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. I would like to express my deep gratitude to my friend and collaborator Professor AndrewWoldar of Villanova University for his professional advice and constant support. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On small world non-Sunada twins and cellular Voronoi diagrams Article published earlier |
| spellingShingle | On small world non-Sunada twins and cellular Voronoi diagrams Ustimenko, V. |
| title | 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_short | On small world non-Sunada twins and cellular Voronoi diagrams |
| title_sort | on small world non-sunada twins and cellular voronoi diagrams |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188557 |
| work_keys_str_mv | AT ustimenkov onsmallworldnonsunadatwinsandcellularvoronoidiagrams |