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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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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. |
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| DOI: | 10.3842/umzh.v76i5.7409 |