On \(k\)-graceful labeling of pendant edge extension of complete bipartite graphs
For any two positive integers \(m,n\), we denote the graph \(K_{m,n}\odot K_1\) by \(G\). Ma Ke-Jie proposed a conjecture [9] that pendant edge extension of a complete bipartite graph is a \(k\)-graceful graph for \(k \ge 2\). In this paper we prove his conjecture for \(n\le m < n^2+\lfloor\f...
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/224 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозиторії
Algebra and Discrete Mathematics| Резюме: | For any two positive integers \(m,n\), we denote the graph \(K_{m,n}\odot K_1\) by \(G\). Ma Ke-Jie proposed a conjecture [9] that pendant edge extension of a complete bipartite graph is a \(k\)-graceful graph for \(k \ge 2\). In this paper we prove his conjecture for \(n\le m < n^2+\lfloor\frac{k}{n}\rfloor+ r\). |
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