Graphs with large Steiner number
UDC 519.1 In 2002, Gary Chartrand and Ping Zhang [The Steiner number of a graph, Discrete Math., 242, 41--54 (2002)] characterized the connected graphs $G$ of order $p \geq 3$ with Steiner number $p$, $p-1,$ or $2.$  In our paper, we characterize all connected graphs $G$ of...
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| Дата: | 2024 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2024
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7409 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512667920236544 |
|---|---|
| author | John, J. Raj, M. S. Malchijah John, J. Raj, M. S. Malchijah |
| author_facet | John, J. Raj, M. S. Malchijah John, J. Raj, M. S. Malchijah |
| author_sort | John, J. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-06-27T08:49:56Z |
| description | UDC 519.1
In 2002, Gary Chartrand and Ping Zhang [The Steiner number of a graph, Discrete Math., 242, 41--54 (2002)] characterized the connected graphs $G$ of order $p \geq 3$ with Steiner number $p$, $p-1,$ or $2.$  In our paper, we characterize all connected graphs $G$ of order $p \geq 4$ with Steiner number  $s(G)=p-2$.  In addition, we obtain some sharp Nordhaus–Gaddum bounds for the Steiner number of connected graphs whose complement is also connected. |
| doi_str_mv | 10.3842/umzh.v76i5.7409 |
| first_indexed | 2026-03-24T03:32:26Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7409 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:26Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-74092024-06-27T08:49:56Z Graphs with large Steiner number Graphs with large Steiner number John, J. Raj, M. S. Malchijah John, J. Raj, M. S. Malchijah Steiner distance, Steiner set, Steiner number UDC 519.1 In 2002, Gary Chartrand and Ping Zhang [The Steiner number of a graph, Discrete Math., 242, 41--54 (2002)] characterized the connected graphs $G$ of order $p \geq 3$ with Steiner number $p$, $p-1,$ or $2.$  In our paper, we characterize all connected graphs $G$ of order $p \geq 4$ with Steiner number  $s(G)=p-2$.  In addition, we obtain some sharp Nordhaus–Gaddum bounds for the Steiner number of connected graphs whose complement is also connected. УДК 519.1 Графи з великим числом Штейнера У 2002 році Гері Чартранд та Пінг Чжан [The Steiner number of a graph, Discrete Math., 242, 41–54 (2002)]  охарактеризували зв'язні графи $G$ порядку $p \geq 3$ з числом Штейнера $p$, $p-1$ або $2.$  У цій статті охарактеризовано всі зв'язні графи $G$ порядку $p \geq 4$ з числом Штейнера $s(G)=p-2$.  Також отримано деякі точні межі Нордгауза\,--\,Гаддума для числа Штейнера зв'язних графів, доповнення яких також є зв'язними. Institute of Mathematics, NAS of Ukraine 2024-06-02 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7409 10.3842/umzh.v76i5.7409 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 5 (2024); 719 - 727 Український математичний журнал; Том 76 № 5 (2024); 719 - 727 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7409/9940 Copyright (c) 2024 Джонсон |
| spellingShingle | John, J. Raj, M. S. Malchijah John, J. Raj, M. S. Malchijah Graphs with large Steiner number |
| title | Graphs with large Steiner number |
| title_alt | Graphs with large Steiner number |
| title_full | Graphs with large Steiner number |
| title_fullStr | Graphs with large Steiner number |
| title_full_unstemmed | Graphs with large Steiner number |
| title_short | Graphs with large Steiner number |
| title_sort | graphs with large steiner number |
| topic_facet | Steiner distance Steiner set Steiner number |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7409 |
| work_keys_str_mv | AT johnj graphswithlargesteinernumber AT rajmsmalchijah graphswithlargesteinernumber AT johnj graphswithlargesteinernumber AT rajmsmalchijah graphswithlargesteinernumber |