On the zero forcing number of graphs and their splitting graphs
In [10], the notion of the splitting graph of a~graph was introduced. In this paper we compute the zero forcing number of the splitting graph of a graph and also obtain some bounds besides finding the exact value of this parameter. We prove for any connected graph \(\Gamma\) of order \(n \ge 2\), \(...
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| Дата: | 2019 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2019
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/496 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | In [10], the notion of the splitting graph of a~graph was introduced. In this paper we compute the zero forcing number of the splitting graph of a graph and also obtain some bounds besides finding the exact value of this parameter. We prove for any connected graph \(\Gamma\) of order \(n \ge 2\), \(Z[S(\Gamma)]\le 2 Z(\Gamma)\) and also obtain many classes of graph in which \(Z[S(\Gamma)]= 2 Z(\Gamma)\). Further, we show some classes of graphs in which \(Z[S(\Gamma)] < 2 Z(\Gamma)\). |
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