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: | Англійська |
| 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| _version_ | 1856543311390572544 |
|---|---|
| author | Chacko, Baby Dominic, Charles Premodkumar, K. P. |
| author_facet | Chacko, Baby Dominic, Charles Premodkumar, K. P. |
| author_sort | Chacko, Baby |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2019-10-20T08:14:09Z |
| description | 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 \(Z[S(\Gamma)] < 2 Z(\Gamma)\). |
| first_indexed | 2025-12-02T15:26:52Z |
| format | Article |
| id | admjournalluguniveduua-article-496 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:26:52Z |
| publishDate | 2019 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-4962019-10-20T08:14:09Z On the zero forcing number of graphs and their splitting graphs Chacko, Baby Dominic, Charles Premodkumar, K. P. zero forcing number, splitting graph, path cover number and domination number of a graph 05C50 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 \(Z[S(\Gamma)] < 2 Z(\Gamma)\). Lugansk National Taras Shevchenko University 2019-10-20 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/496 Algebra and Discrete Mathematics; Vol 28, No 1 (2019) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/496/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/496/226 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/496/227 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/496/228 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/496/229 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/496/231 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/496/597 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/496/599 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/496/600 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/496/601 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/496/602 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/496/603 Copyright (c) 2019 Algebra and Discrete Mathematics |
| spellingShingle | zero forcing number splitting graph path cover number and domination number of a graph 05C50 Chacko, Baby Dominic, Charles Premodkumar, K. P. On the zero forcing number of graphs and their splitting graphs |
| title | On the zero forcing number of graphs and their splitting graphs |
| title_full | On the zero forcing number of graphs and their splitting graphs |
| title_fullStr | On the zero forcing number of graphs and their splitting graphs |
| title_full_unstemmed | On the zero forcing number of graphs and their splitting graphs |
| title_short | On the zero forcing number of graphs and their splitting graphs |
| title_sort | on the zero forcing number of graphs and their splitting graphs |
| topic | zero forcing number splitting graph path cover number and domination number of a graph 05C50 |
| topic_facet | zero forcing number splitting graph path cover number and domination number of a graph 05C50 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/496 |
| work_keys_str_mv | AT chackobaby onthezeroforcingnumberofgraphsandtheirsplittinggraphs AT dominiccharles onthezeroforcingnumberofgraphsandtheirsplittinggraphs AT premodkumarkp onthezeroforcingnumberofgraphsandtheirsplittinggraphs |